Find $\frac{d}{dx}\left(x^2{e}^x\right)$ and evaluate it at $x=3$.

Step-by-step solution

1. Apply the product rule: $\frac{d}{dx}(x^2{e}^x)=2x{e}^x+x^2{e}^x$.
2. Factor out $e^x$: $e^x(2x+x^2)$.
3. Substitute $x=3$: $e^3(6+9)=15e^3$.

Concept tested: Product rule differentiation

Published 3 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

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