{"id":12748,"date":"2022-04-29T18:12:20","date_gmt":"2022-04-29T13:12:20","guid":{"rendered":"https:\/\/www.vuassistance.com\/?p=12748"},"modified":"2022-04-29T18:13:36","modified_gmt":"2022-04-29T13:13:36","slug":"what-is-derivative-in-calculus-explained-with-examples","status":"publish","type":"post","link":"https:\/\/www.vuassistance.com\/what-is-derivative-in-calculus-explained-with-examples\/","title":{"rendered":"What is derivative in calculus? Explained with examples"},"content":{"rendered":"<p><span style=\"font-weight: 400\">A derivative is a branch of calculus used to find the slope of the tangent line. It usually differentiates the linear, quadratic, constant, and polynomial functions with respect to its independent variables.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">The derivative can also be used to differentiate the linear or polynomial equations and the multivariable functions. It can be defined by using the limits. The limit is also a branch of calculus used to find the numerical value of a function at a specific point.<\/span><\/p>\n<p><span style=\"font-weight: 400\">In this article, we will learn the definition, notation, formula, rules, and examples of derivatives along with a lot of examples.<\/span><\/p>\n<h2><b>What is derivative?<\/b><\/h2>\n<p><span style=\"font-weight: 400\">In calculus, the <\/span><a href=\"https:\/\/www.brightstorm.com\/math\/calculus\/the-derivative\/the-definition-of-the-derivative\/\"><span style=\"font-weight: 400\">derivative<\/span><\/a><span style=\"font-weight: 400\"> is the slope of a line that lies tangent to the curve at a specific point. It can also be defined as the instantaneous rate of change of function as it approaches to zero by applying the limit.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">The derivative can find the differential of the exponential function, polynomial function, constant function, linear function, logarithmic function, or the trigonometric function.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">The derivative has various types to solve complex calculus problems. The types of differentiation are:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The explicit derivative<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The implicit derivative<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The partial derivative<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The directional derivative&nbsp;<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">All the above types of derivatives have different techniques to find the derivative of various kinds of functions and equations. The explicit derivative is the main type of derivative that is used to find the derivative of a one-variable function.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">The equation and multivariable functions are not involved in this type of differentiation. It is denoted by d\/dx or f\u2019(x). Implicit differentiation is the second type of derivative that is used to find the derivative of the implicit function or equation.<\/span><\/p>\n<p><span style=\"font-weight: 400\">In this type of derivative, differential notation is applied on both sides of the equation. It differentiates the function of y in terms of x without taking it as a constant. It is denoted by dy\/dx or y\u2019(x).<\/span><\/p>\n<p><span style=\"font-weight: 400\">The third type of derivative is the partial derivative that deals with the multivariable function. the function f(x, y, z) can be differentiated with respect to x, y, or z. It is denoted by \u2202f(x, y, z) \/ \u2202x, \u2202f(x, y, z) \/ \u2202y, or \u2202f(x, y, z) \/ \u2202z.<\/span><\/p>\n<p><span style=\"font-weight: 400\">The directional derivative is also a type of derivative that is used to find the direction of the function by taking the dot product of the gradient and the normalized vector. It is denoted by \u2202<\/span><span style=\"font-weight: 400\">u<\/span><span style=\"font-weight: 400\"> f(x, y, z).<\/span><\/p>\n<h2><b>Rules of differentiation<\/b><\/h2>\n<p><span style=\"font-weight: 400\">There are various rules of differentiation used to solve the problems of the derivative. These rules are:<\/span><\/p>\n<ul>\n<li><b>The sum rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [h(x) + g(x)] = d\/dx [h(x)] + d\/dx [g(x)]<\/span><\/p>\n<ul>\n<li><b>The constant rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [C] = 0<\/span><\/p>\n<ul>\n<li><b>The difference rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [h(x) &#8211; g(x)] = d\/dx [h(x)] &#8211; d\/dx [g(x)]<\/span><\/p>\n<ul>\n<li><b>The power rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [h<\/span><span style=\"font-weight: 400\">n<\/span><span style=\"font-weight: 400\">(x)] = nh<\/span><span style=\"font-weight: 400\">n-1<\/span><span style=\"font-weight: 400\">(x) * d h(x)\/dx<\/span><\/p>\n<ul>\n<li><b>The product rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [h(x) * g(x)] = g(x) d\/dx [h(x)] + f(x) d\/dx [g(x)]<\/span><\/p>\n<ul>\n<li><b>The quotient rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [h(x) + g(x)] = 1\/[g(x)]<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> [g(x) d\/dx [h(x)] &#8211; f(x) d\/dx [g(x)]]<\/span><\/p>\n<ul>\n<li><b>The constant function rule<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">d\/dx [C h(x)] = C * d\/dx [h(x)]<\/span><\/p>\n<h2><b>How to find the derivative of functions?<\/b><\/h2>\n<p><span style=\"font-weight: 400\">By using the rules of differentiation, you can easily solve any problem of derivative. Below are a few examples of derivatives.<\/span><\/p>\n<p><b>Example 1: For Explicit differentiation.<\/b><\/p>\n<p><span style=\"font-weight: 400\">Find the derivative of 2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2, with respect to z?<\/span><\/p>\n<p><b>Solution&nbsp;<\/b><\/p>\n<p><b>Step 1:<\/b> <span style=\"font-weight: 400\">First of all, write the given function.<\/span><\/p>\n<p><span style=\"font-weight: 400\">f(z) = 2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2<\/span><\/p>\n<p><b>Step 2:<\/b> <span style=\"font-weight: 400\">Apply the notation of derivative (d\/dz) to the given function.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [f(z)] = d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2]<\/span><\/p>\n<p><b>Step 3:<\/b> <span style=\"font-weight: 400\">Now apply the notation of derivative separately to each function by using the sum and difference rules of differentiation.<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + d\/dz [13z] \u2013 d\/dz [4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] + d\/dz [cos(z)] + d\/dz [2]<\/span><\/p>\n<p><b>Step 4:<\/b> <span style=\"font-weight: 400\">Now differentiate the above expression by using the power, constant, trigonometry, and the constant function rule of differentiation.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = 2d\/dz [z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + 13d\/dz [z] \u2013 4d\/dz [z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] + d\/dz [cos(z)] + d\/dz [2]<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = 2 [2z<\/span><span style=\"font-weight: 400\">2-1<\/span><span style=\"font-weight: 400\">] + 13[z<\/span><span style=\"font-weight: 400\">1-1<\/span><span style=\"font-weight: 400\">] \u2013 4 [3z<\/span><span style=\"font-weight: 400\">3-1<\/span><span style=\"font-weight: 400\">] + [-sin(z)] + [0]<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = 2 [2z<\/span><span style=\"font-weight: 400\">1<\/span><span style=\"font-weight: 400\">] + 13[z<\/span><span style=\"font-weight: 400\">0<\/span><span style=\"font-weight: 400\">] \u2013 4 [3z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + [-sin(z)] + [0]<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = 2 [2z] + 13[1] \u2013 4 [3z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + [-sin(z)] + [0]<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = 4z + 13 \u2013 12z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> &#8211; sin(z) + 0<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dz [2z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 13z \u2013 4z<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> + cos(z) + 2] = 4z + 13 \u2013 12z<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> &#8211; sin(z)&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">You can use a <\/span><a href=\"https:\/\/www.allmath.com\/derivative.php\"><span style=\"font-weight: 400\">derivative calculator<\/span><\/a><span style=\"font-weight: 400\"> to find the derivative of any function in a fraction of seconds with steps. Follow the below steps to differentiate the functions by using this tool.<\/span><\/p>\n<p><b>Step 1:<\/b><span style=\"font-weight: 400\"> Input the function.<\/span><\/p>\n<p><b>Step 2:<\/b><span style=\"font-weight: 400\"> Select the independent variable.<\/span><\/p>\n<p><b>Step 3:<\/b><span style=\"font-weight: 400\"> Write the order of derivatives.<\/span><\/p>\n<p><b>Step 4<\/b><span style=\"font-weight: 400\">: Click the calculate button.<\/span><\/p>\n<p><b>Step 5:<\/b><span style=\"font-weight: 400\"> The result with steps will show below the calculate button.<\/span><\/p>\n<p><b>Example 2: For implicit differentiation<\/b><\/p>\n<p><span style=\"font-weight: 400\">Fid the derivative of 12xy<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 2y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> \u2013 4y<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\"> = (4x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> * 2x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">) + 7x + 3y, with respect to x?<\/span><\/p>\n<p><b>Solution<\/b><\/p>\n<p><b>Step 1:<\/b> <span style=\"font-weight: 400\">First of all, write the given function.<\/span><\/p>\n<p><span style=\"font-weight: 400\">12xy<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 2y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> \u2013 4y<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\"> = (4x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> * 2x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">) + 7x + 3y<\/span><b>&nbsp;<\/b><\/p>\n<p><b>Step 2:<\/b> <span style=\"font-weight: 400\">Apply the notation of derivative (d\/dx) on the both sides of the given function.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dx [12xy<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 2y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> \u2013 4y<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\">] = d\/dx [(4x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> * 2x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">) + 7x + 3y]<\/span><\/p>\n<p><b>Step 3:<\/b> <span style=\"font-weight: 400\">Now apply the notation of derivative separately to each function by using the sum, product, and difference rules of differentiation.<\/span><\/p>\n<p><span style=\"font-weight: 400\">d\/dx [12xy<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + d\/dx [2y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] \u2013 d\/dx [4y<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\">] = d\/dx [(4x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> * 2x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">)] + d\/dx [7x] + d\/dx [3y]<\/span><\/p>\n<p><span style=\"font-weight: 400\">y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">d\/dx [12x] + 12xd\/dx[y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + d\/dx [2y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] \u2013 d\/dx [4y<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\">] = 2x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">d\/dx [4x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\">] + 4x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\">d\/dx [2x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] + d\/dx [7x] + d\/dx [3y]<\/span><\/p>\n<p><b>Step 4:<\/b> <span style=\"font-weight: 400\">Now differentiate the above expression by using the power, constant, and the constant function rule of differentiation.<\/span><\/p>\n<p><span style=\"font-weight: 400\">12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">d\/dx [x] + 12xd\/dx[y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + 2d\/dx [y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] \u2013 4d\/dx [y<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\">] = 8x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">d\/dx [x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\">] + 8x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\">d\/dx [x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\">] + 7d\/dx [x] + 3d\/dx [y]<\/span><\/p>\n<p><span style=\"font-weight: 400\">12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> [1] + 12x [2y<\/span><span style=\"font-weight: 400\">2-1<\/span><span style=\"font-weight: 400\"> dy\/dx] + 2 [3y<\/span><span style=\"font-weight: 400\">3-1<\/span><span style=\"font-weight: 400\"> dy\/dx] \u2013 4 [4y<\/span><span style=\"font-weight: 400\">4-1<\/span><span style=\"font-weight: 400\"> dy\/dx] = 8x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> [5x<\/span><span style=\"font-weight: 400\">5-1<\/span><span style=\"font-weight: 400\">] + 8x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> [3x<\/span><span style=\"font-weight: 400\">3-1<\/span><span style=\"font-weight: 400\">] + 7 [1] + 3 [dy\/dx]<\/span><\/p>\n<p><span style=\"font-weight: 400\">12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> [1] + 12x [2y dy\/dx] + 2 [3y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> dy\/dx] \u2013 4 [4y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> dy\/dx] = 8x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> [5x<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\">] + 8x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> [3x<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + 7 [1] + 3 [dy\/dx]<\/span><\/p>\n<p><span style=\"font-weight: 400\">12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 12x [2y dy\/dx] + 2 [3y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> dy\/dx] \u2013 4 [4y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> dy\/dx] = 8x<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> [5x<\/span><span style=\"font-weight: 400\">4<\/span><span style=\"font-weight: 400\">] + 8x<\/span><span style=\"font-weight: 400\">5<\/span><span style=\"font-weight: 400\"> [3x<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">] + 7 + 3 [dy\/dx]<\/span><\/p>\n<p><span style=\"font-weight: 400\">12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 24xy dy\/dx + 6y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> dy\/dx \u2013 16y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> dy\/dx = 40x<\/span><span style=\"font-weight: 400\">7<\/span><span style=\"font-weight: 400\"> + 24x<\/span><span style=\"font-weight: 400\">7<\/span><span style=\"font-weight: 400\"> + 7 + 3dy\/dx<\/span><\/p>\n<p><span style=\"font-weight: 400\">12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> + 24xy dy\/dx + 6y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> dy\/dx \u2013 16y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> dy\/dx = 64x<\/span><span style=\"font-weight: 400\">7<\/span><span style=\"font-weight: 400\"> + 7 + 3dy\/dx<\/span><\/p>\n<p><b>Step 5:<\/b> <span style=\"font-weight: 400\">Now take the dy\/dx term on same side of the equation.<\/span><\/p>\n<p><span style=\"font-weight: 400\">24xy dy\/dx + 6y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\"> dy\/dx \u2013 16y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> dy\/dx &#8211; 3dy\/dx = 64x<\/span><span style=\"font-weight: 400\">7<\/span><span style=\"font-weight: 400\"> + 7 &#8211; 12y<\/span><span style=\"font-weight: 400\">2<\/span><\/p>\n<p><span style=\"font-weight: 400\">(24xy + 6y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">\u2013 16y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> \u2013 3) dy\/dx = 64x<\/span><span style=\"font-weight: 400\">7<\/span><span style=\"font-weight: 400\"> + 7 &#8211; 12y<\/span><span style=\"font-weight: 400\">2<\/span><\/p>\n<p><span style=\"font-weight: 400\">dy\/dx = (64x<\/span><span style=\"font-weight: 400\">7<\/span><span style=\"font-weight: 400\"> + 7 &#8211; 12y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">) \/ (24xy + 6y<\/span><span style=\"font-weight: 400\">2<\/span><span style=\"font-weight: 400\">\u2013 16y<\/span><span style=\"font-weight: 400\">3<\/span><span style=\"font-weight: 400\"> \u2013 3)<\/span><\/p>\n<h2><b>Summary&nbsp;<\/b><\/h2>\n<p><span style=\"font-weight: 400\">In this post, we have learned almost all the basics of the derivative in calculus. Now you can solve any problem of derivative either by explicit differentiation or implicit differentiation easily by learning the rules and examples of this article.<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A derivative is a branch of calculus used to find the slope of the tangent line. It usually differentiates the linear, quadratic, constant, and polynomial [&hellip;] <span class=\"read-more-link\"><a class=\"read-more\" href=\"https:\/\/www.vuassistance.com\/what-is-derivative-in-calculus-explained-with-examples\/\">Read More<\/a><\/span><\/p>\n","protected":false},"author":20,"featured_media":13029,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[536],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/posts\/12748"}],"collection":[{"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/comments?post=12748"}],"version-history":[{"count":3,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/posts\/12748\/revisions"}],"predecessor-version":[{"id":13033,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/posts\/12748\/revisions\/13033"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/media\/13029"}],"wp:attachment":[{"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/media?parent=12748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/categories?post=12748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vuassistance.com\/wp-json\/wp\/v2\/tags?post=12748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}