Question

Calcular a derivada abaixo:
h(t)= 2 cos √t

Answer 1

$\mathrm{h(t)=2\cos{\sqrt{t}}}}\\\\ \mathrm{*\ y=f(g(x))\ \to\ \dfrac{dy}{dx}=f'(g(x)).g'(x)}}\\\\ \mathrm{h'(t)=2\dfrac{d}{dt}(\cos{\sqrt{t}})=2(-\sin{\sqrt{t}})\dfrac{d}{dt}(\sqrt{t})=}\\\\ \mathrm{=-2\sin{\sqrt{t}}\dfrac{1}{2\sqrt{t}}\ \to\ \boxed{\mathbf{h'(t)=-\dfrac{\sin{\sqrt{t}}}{\sqrt{t}}}}}$