Question

Qual a derivada de e^2x*x?

Answer 1

Aqui, vamos usar a regra do produto:

$f(x)=e^{2x}\cdot x$

_________

Derivando,

$f'(x)=\big(e^{2x}\cdot x\big)'\\\\ f'(x)=\big(e^{2x}\big)'\cdot x+e^{2x}\cdot (x)'\\\\ f'(x)=\big(e^{2x}\cdot (2x)'\big)\cdot x+e^{2x}\cdot 1\\\\ f'(x)=\big(e^{2x}\cdot 2\big)\cdot x+e^{2x}\cdot 1\\\\ f'(x)=2x\,e^{2x}+e^{2x}\\\\\\ \therefore~~\boxed{\begin{array}{c} f'(x)=(2x+1)\,e^{2x} \end{array}}$


Bons estudos! :-)