Question

Derivada de f(x) = x².e×

Answer 1

Resposta:

Sabemos que:

$\frac{d}{dx} \left( x^2 \right) = 2x;\\\\\frac{d}{dx} \left( a^x \right) = a^x \cdot ln(a).$

Aplicando a regra do produto, temos:

$\frac{d}{dx} \left( x^2 \cdot e^x \right) = \\\\ = x^2 \left(e^x \cdot ln(e) \right) + e^x (2x)\\\\= x^2 \left(e^x \cdot 1 \right) + 2xe^x\\\\= \boxed{x^2e^x + 2xe^x.}$