differentiate x^2*e^x — step-by-step solution

Let's differentiate:

{(x^{2} e^{x})}^{'}

We differentiate

U1

x^{2}

and

V2

e^{x}

using:

{(U1 \cdot V2)}^{'} = {(U1)}^{'} \cdot V2 + U1 \cdot {(V2)}^{'}

Let's differentiate

U1

{(x^{2})}^{'}

2 x

Let's perform the differentiation

V2

{(e^{x})}^{'}

e^{x}

Then you can resume the differentiation:

2 x e^{x} + x^{2} e^{x}

e^{x} x^{2} + 2 e^{x} x

You can factorize this expression into:

e^{x} x \cdot (x + 2)

▷Answer: $e^{x} x \cdot (x + 2)$