Derivatives of Composite Functions
1. What is Composite Function?
Composite Function is a function in which the variable of the function is itself a function. Composite function is represented as, h(x) = f(g(x))
2. What are Examples of Composite Functions?
Examples of Composite Functions are,
- sin (x2 + 2x)
- 2(cos x)2 + 3
- esin x, etc
3. What is Derivative of Composite Function?
Derivative of Composite Function is the derivative of function that are composite. The derivative of composite function is found using the chain rule.
4. What is Derivative of Composite Function Formula?
Derivative of Composite Function Formula is added below,
d/dx{f(g(x))} = f'(g(x)).d/dx(g(x))
Derivatives of Composite Functions
Derivatives are an essential part of calculus. They help us in calculating the rate of change, maxima, and minima for the functions. Derivatives by definition are given by using limits, which is called the first form of the derivative. We already know how to calculate the derivatives for standard functions, but sometimes we need to deal with complex mathematical functions that are composed of more than two functions. It becomes hard to calculate the derivative for such functions in the normal way. It becomes essential to learn about the rules and methods which make our calculation easier. The chain rule is one of them, which allows us to calculate the derivatives of complex functions.
In this article, we will learn about derivatives of Composite Functions, Examples, and others in detail.
Table of Content
- What is Derivative of Composite Functions?
- Derivatives of Composite Functions Formula
- Composite Functions and Chain Rule
- Chain Rule
- Alternative Method to Chain Rule
- Derivatives of Composite Functions In One Variable
- Derivatives of Composite Functions Examples
- Practice Questions
- FAQs on Derivatives
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