What is Derivative of Composite Functions?

What is Derivative of Composite Functions?

Derivative of Composite Function is the derivative of the function that is composite. A composite function is a function in which the variable is itself a function of the variable. The derivative of these functions is easily found using the derivative of the composite function formula that is explained below in the article....

Derivatives of Composite Functions Formula

Suppose we have a composite function h(x) that is represented as, h(x) = f{g(x)}, then first we find the derivative of f(x) and multiply the same with the derivative of g(x) to get the required derivative of the composite function....

Composite Functions and Chain Rule

Let’s say we have a function f(x) = (x + 1)2, for which we want to calculate the derivative. These kinds of functions are called composite functions, which means they are made up of more than one function. Usually, they are of the form g(x) = h(f(x)) or it can also be written as g = hof(x). In our case, the given function f(x) = (x + 1)2 is composed of two functions,...

Chain Rule

Let f be a real-valued function which is a composite of two functions, “u” and “v”, that is f = v o u. Let’s say t = u(x) and if both dv/dt and dt/dx exist for both of the functions “u” and “v”....

Alternative Method to Chain Rule

The chain rule can also be applied with a shortcut method. This is explained with an example, let’s say we have a function f(x) = (sin(x))2...

Derivatives of Composite Functions In One Variable

Using the chain rule the derivative of composite function in one variable is easily find. This is explained as by the example, find the derivative of (x2 + 3)3...

Derivatives of Composite Functions Examples

Examples 1: Find the derivative for the function f(x) = (x + 1)2....

Practice Questions on Derivative of Composite Functions

Q1: Differentiate sin(log x)...

FAQs on Derivatives of Composite Functions

1. What is Composite Function?...