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

Let's differentiate:

\frac{d}{d x} (x^{2} e^{x})

For

u1

x^{2}

and

v2

e^{x}

, use the differentiation rule:

\frac{d}{d x} (u1 \cdot v2) = \frac{d}{d x} (u1) \cdot v2 + u1 \cdot \frac{d}{d x} (v2)

Let's perform the differentiation

u1

\frac{d}{d x} (x^{2})

ⓘ The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{2})

2 x

2 x

Let's differentiate

v2

\frac{d}{d x} (e^{x})

ⓘ The derivative of exp(x) is exp(x):

\frac{d}{d x} (e^{x})

e^{x}

e^{x}

Then you can resume the derivation:

ⅰ

\frac{d}{d x} (x^{2} e^{x})

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

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

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

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

▶Derivative:

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