The product rule

Differentiation

A-level Maths (9MA0)

ORIGINAL

Differentiate a product of two functions — then factorise, because the mark scheme wants it tidy.

Board and spec code confirmed against Edexcel 9MA0 · registry checked 2026-07-11How this checking works

Question

Differentiate

y = x^2 e^x

with respect to

x

Every step worked, with the reasoning.

1
Let $u = x^2$ and $v = e^x$ .
It's a product of two functions of $x$ .
2
$u' = 2x$ and $v' = e^x$
Differentiate each factor.
3
$\dfrac{dy}{dx} = u'v + uv' = 2x\,e^x + x^2 e^x$
Product rule: $u'v + uv'$ .
4
$\dfrac{dy}{dx} = x e^x(x + 2)$
Factor out $x e^x$ .

Answer: $\dfrac{dy}{dx} = x e^x(x + 2)$

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