Double Chain Rule of Differentiation
We are going to learn Double Chain Rule of Differentiation.
For a function where it is dependent on more than one variable. i.e. the nesting of function occurs, chain rule of differentiation fails in such a situation double chain rule is applied.
Now for any three functions p, q, and r and a composite function f where f is a composite of p, q, and r such that, f = (p o q) o r, i.e. f(x) = p[q{r(x)}], then its derivative is given as,
df/dx = df/dp. dp/dq. dq/dr. dr/dx
Let’s understand the Double Chain Rule with the help of an example :
Example: Differentiate, y = (sin 2x)2
Solution:
y = (sin 2x)2
y’ = 2( sin 2x) . (cos 2x). (2)
= 4 sin2x . cos 2x
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
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