Chain Rule Steps to find the Derivative
We have explained the steps to find the derivative of Chain Rule. Below is the steps to find the derivative of function Sin(x²).
Step 1: Check to see if the function is a composite function, meaning it comprises a function within a function. The function Sin(x2) is a composite function.
Step 2: Determine the outer f(x) and inner functions g(x). f(x) = Sin(x) and g(x) = x² in this case.
Step 3: Now only look for the differentiation of the outer function. In this case, f'(x) = Cos (x).
Step 4: Now only look for the differentiation of the inner function. In this case, g'(x) = 2x.
Step 5: Find the product of f'(x) and g'(x) here, which is (2x)Cos(x).
We found the derivative of Sin(x2), which is (2x)Cos using the Chain rule (x).
Chain Rule: Theorem, Formula and Solved Examples
Chain Rule is a way to find the derivative of composite functions. It is one of the basic rules used in mathematics for solving differential problems. It helps us to find the derivative of composite functions such as (3x2 + 1)4, (sin 4x), e3x, (ln x)2, and others. Only the derivatives of composite functions are found using the chain rule. The famous German scientist, Gottfried Leibniz gave the chain rule in the early 17th century.
Let’s learn about Chain Rule formula, derivation and examples in detail below.
Table of Content
- What is Chain Rule?
- Chain Rule Theorem
- Chain Rule Steps to find the Derivative
- Chain Rule Formula
- Chain Rule Formula Proof
- Double Chain Rule of Differentiation
- Chain Rule for Partial Derivatives
- Application of Chain Rule
- Chain Rule Derivative Solved Examples
- Chain Rule Derivative Practice Problems
- Chain Rule Differential – FAQs