Calculus

Forgetting to Apply the Chain Rule

Students differentiate the outside function but forget to multiply by the derivative of the inside function.

Quick check

Why students make it

They treat a composite function like a simple power, trig, exponential, or root function. The outside pattern feels familiar, so the inside function gets left unchanged.

The rule done right

For a composite function f(g(x))f(g(x)), use the chain rule: ddxf(g(x))=f′(g(x))⋅g′(x)\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x). Differentiate the outside, keep the inside, then multiply by the derivative of the inside.

Related resources

chain-rulederivativescomposite-functions