Question

Qual a derivada da função:
f(x)=(e^(2x))/(x^(2))

Answer 1

Resposta:

Explicação passo-a-passo:

Basta usar a regra do quociente

$y=\dfrac{u}{v}\\\\\\y'=\dfrac{u'.v-u.v'}{v^{2}}$

$f(x)=\dfrac{e^{2x}}{x^{2}}\\\\Derivando\\\\f'(x)=\dfrac{(e^{2x}.2).x^{2}-e^{2x}.2x}{(x^{2})^{2}}\\\\\\f'(x)=\dfrac{2x^{2}.e^{2x}-2xe^{2x}}{x^{4}}\\\\\\f'(x)=\dfrac{x.(2x.e^{2x}-2e^{2x})}{x^{4}}\\\\\\f'(x)=\dfrac{2x.e^{2x}-2e^{2x}}{x^{3}}\\\\\\f'(x)=\dfrac{2.e^{2x}(x-1)}{x^{3}}$