Question

derivada de f(x) = sen ³ $4 x^{5}$

Answer 1

Olá, Danielatd.

Façamos:

$\begin{cases}f(x)=x^3\\g(x)=\sin x\\h(x)=4x^5\end{cases}\Rightarrow \sin^34x^5=f(g(h(x)))$

Apliquemos agora a Regra da Cadeia, ou seja:

$\frac{d}{dx}[f(g(h(x)))]=f'(g(h(x)))\cdot g'(h(x))\cdot h'(x)=\\\\=(3\sin^24x^5)\cdot (\cos4x^5)\cdot20x^4=$

$=60x^4\sin^24x^5\cdot\cos4x^5$