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Step-by-step calculus

Chain Rule Calculator

Differentiate composite functions by identifying the inner and outer functions, then multiplying their derivatives.

Works in your browserSteps explainedVideo explanations

Learn the method

Work from the outside in

Name each layer and multiply by the derivative of what is inside it.

ddxsin⁡(x2)=cos⁡(x2)⋅2x\frac{d}{dx}\sin(x^2)=\cos(x^2)\cdot2x
Calculus formulas

Worked example

  1. 1Outer function: f(u)=sin(u). Inner function: u=x².
  2. 2Differentiate the outside and keep the inside: f′(u)=cos(u).
  3. 3Multiply by u′=2x: the result is 2x cos(x²).

For three or more nested layers, keep multiplying by the next inner derivative until you reach x.

What this chain rule calculator does

  • Label inner and outer functions before differentiating.
  • Work through several nested layers one at a time.
  • Combine the chain rule with product and quotient rules.
  • Check restrictions for logarithms, roots and denominators.

How to use it

  1. Enter a function or equation, or use the formula keyboard or a photo.
  2. Check the variable and differentiation settings, then press Solve.
  3. Read the steps, ask a follow-up question, or create a video lesson from the result.

Questions about the chain rule calculator

What is the chain rule?

If y=f(g(x)), then dy/dx=f′(g(x))g′(x), wherever the component functions are differentiable. The inner derivative must be included.

Does this calculator show steps?

Yes. The solver explains the rules and intermediate expressions. AI can make mistakes; check the assumptions and each step.

Can I generate a video explanation?

After solving, choose Video lesson to generate a narrated whiteboard explanation. Generation is subject to the displayed quota.