Chain Rule Calculator

Enter u(v(x)), v(x) separated by a comma (e.g., sin(x^2), x^2) to compute the derivative using the chain rule.

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)