Question

Como posso resolver esta questão?

Answer 1

Olá, Tynna.

Aplique a regra da cadeia.

$h(x)=5x,g(x)=\cos x,f(x)=\sqrt{x} \Rightarrow\sqrt{\cos 5x}=f(g(h(x)))\\\\ \text{Regra da cadeia: }\frac{d}{dx}[f(g(h(x)))]=f'(g(h(x)))\cdot g'(h(x))\cdot h'(x)$

$\sqrt{\cos 5x}=(\cos 5x)^{\frac12}\\\\\frac{d}{dx}(\cos 5x)^\frac12=\\\\ =\frac12(\cos5x)^{-\frac12}\cdot(-\sin5x)\cdot 5=\\\\ =\frac{1}{2\sqrt{\cos 5x}}\cdot(-5\sin 5x)=\\\\ =-\frac{5\sin 5x\sqrt{\cos 5x}}{2\cos 5x}=\\\\ =-\frac52(\tan 5x)(\sqrt{\cos 5x})$