Chain Rule Calculator

This Chain Rule Calculator helps you differentiate composite functions and shows each step clearly. It applies the chain rule to expressions where one function is inside another by differentiating the outer function, differentiating the inner function, and then multiplying the results correctly. This makes it useful for checking answers, understanding how the rule works, and practising calculus step by step.

Step-by-step method

1. Set up the problem.
2. Differentiate the outer and inner parts.
3. Multiply u'(v(x)) by v'(x).

Formula:

Example 1: u(v(x)) = sin(x^2), v(x) = x^2

Step 1 - Set up the problem.

In this problem: Identify the outer u and inner v, then use the chain rule structure.

Step 2 - Differentiate the outer and inner parts.

In this problem: Compute u'(v(x)) and v'(x).

Step 3 - Apply the chain rule.

In this problem: Multiply u'(v(x)) by v'(x).

Final answer: f'(x) = 2xcos(x^2)

Example 2: u(v(x)) = log(3x + 1), v(x) = 3x + 1

Step 1 - Set up the problem.

In this problem: Identify the outer u and inner v, then use the chain rule structure.

Step 2 - Differentiate the outer and inner parts.

In this problem: Compute u'(v(x)) and v'(x).

Step 3 - Apply the chain rule.

In this problem: Multiply u'(v(x)) by v'(x).

Final answer: f'(x) = 3/(3x + 1)