Question

determinar as derivadas das funçoes f(x) sen raiz x?

Answer 1

Boa noite!

Supondo ser a função:
$f(x)=\sin\sqrt{x}\\f'(x)=\left(\sin\sqrt{x}\right)'\\f'(x)=\cos\sqrt{x}\cdot\left(\sqrt{x}\right)'\\f'(x)=\cos\sqrt{x}\cdot\left(x^{^1/_2}\right)'\\f'(x)=\cos\sqrt{x}\cdot\left(\dfrac{1}{2}-1\right)\cdot{x^{^1/_2-1}}\\f'(x)=\cos\sqrt{x}\cdot\dfrac{-1}{2}\cdot{x^{-1/2}}\\f'(x)=\cos\sqrt{x}\cdot\dfrac{-1}{2\sqrt{x}}\\f'(x)=\dfrac{-\cos\sqrt{x}}{2\sqrt{x}}$

Espero ter ajudado!