The chain rule mistakes that cost you the A*

Published 2026-03-25 · Written by Pete Bromfield

Six real Edexcel scripts I marked last year. Six chain-rule mistakes. Spot yours before Paper 1.

Setup — differentiate $y = (3x^2 + 1)^4$

Correct answer: $\dfrac{dy}{dx} = 4(3x^2 + 1)^3 \cdot 6x = 24x(3x^2 + 1)^3$.

The 6 wrong answers I saw

1. $4(3x^2 + 1)^3$ — forgot to multiply by the derivative of the inner function.
2. $4(3x^2 + 1)^3 \cdot 3x$ — differentiated $3x^2$ wrongly.
3. $12x^2(3x^2 + 1)^3$ — differentiated $3x^2$ as $3x^2$ (i.e. didn't differentiate at all).
4. $24x(3x^2)^3$ — dropped the $+1$ inside the bracket.
5. $4(6x)^3$ — flattened both parts into a single power.
6. $(24x)(3x^2 + 1)^4$ — kept the power the same instead of dropping by 1.

The rule you need on lockdown

Chain rule: $\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}$. Say it out loud every time you meet a bracketed function.

10 chain-rule drills on Skills Practice → Differentiation. And bookmark the ones that catch you.