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

Let's differentiate:

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

We differentiate

U1

x

and

V2

e^{x}

using:

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

Let's perform the differentiation

U1

{(x)}^{'}

1

Let's perform the differentiation

V2

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

e^{x}

You can evaluate the resulted derivative (

U1 \cdot V2

)':

1 \cdot e^{x} + x e^{x}

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

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

This expression can be factorized into:

e^{x} \cdot (x + 1)

▷Answer: $e^{x} \cdot (x + 1)$