Question

Calcular a derivada das seguintes funções( cadeia com três funções)
$y= e^{sen(4x)}$

Answer 1

e^{sen(4x)} . Cos(4x) . 4

Answer 2

$\mathrm{y=e^{\sin(4x)}\ \ \| \ \ \dfrac{dy}{dx}=\ ?}\\\\ \textrm{Usando a regra da cadeia, teremos que:}\\\\ \mathrm{y=f(g(h(x)))\ \to\ \dfrac{dy}{dx}=f'(g(h(x))).g'(h(x)).h'(x)}\\\\ \mathrm{f(x)=e^x\ \ \| \ \ g(x)=\sin(x)\ \ \| \ \ h(x)=4x}\\\\ \mathrm{\dfrac{dy}{dx}=\dfrac{d}{dx}(e^{\sin(4x)}).\dfrac{d}{dx}(\sin(4x)).\dfrac{d}{dx}(4x)=}\\\\ \mathrm{=e^{\sin(4x)}.\cos(4x).4=\mathbf{4.e^{\sin(4x)}.\cos(4x)}}$