differentiate x^3*e^x — step-by-step solution

Let's perform the differentiation:

{(x^{3} e^{x})}^{'}

For

U1

x^{3}

and

V2

e^{x}

, use the product/quotient rule:

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

Let's differentiate

U1

{(x^{3})}^{'}

3 x^{2}

Let's differentiate

V2

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

e^{x}

Then you can continue the differentiation:

3 x^{2} e^{x} + x^{3} e^{x}

e^{x} x^{3} + 3 e^{x} x^{2}

This expression can be factorized into:

e^{x} x^{2} \cdot (x + 3)

▷Result: $e^{x} x^{2} \cdot (x + 3)$