Question

Qual a derivada da função : f(x) = e^sen4x

Answer 1

Olá, Júnior.

Faça: f(x) = $e^x$, g(x) = sen x e h(x) = 4x.

Utilize, agora, a regra da cadeia:

[f(g(h(x)))]' = f'(g(h(x))) . g'(h(x))) . h'(x) = $\boxed{e^{sen 4x}\cdot cos\,{4x}\cdot4}$

Answer 2

$f(x)=e^t\\ \\ t=sen(4x)\\ \\ t=sen(u)\\ \\ u=4x\\ \\ \frac{dy}{dx}=\frac{dy}{dt}*\frac{dt}{du}*\frac{du}{dx}\\ \\ \frac{dy}{dx}=e^t*cos(u)*4\\ \\ \frac{dy}{dx}=e^{sen(4x)}*cos(4x)*4\\ \\ \frac{dy}{dx}=4e^{sen(4x)}*cos(4x)$