Question

Derivada: f(t) = 2t/2+raiz t

Answer 1

Regra do quociente

$f(t)=\frac{2t}{2+\sqrt{t}}\\\\ f'(t)=\frac{2(2+\sqrt{t})-2t(\frac{1}{2\sqrt{t}}}{(2+\sqrt{t})^2}$

$f'(t)=\frac{2(2+\sqrt{t})-\frac{t}{\sqrt{t}}}{(2+\sqrt{t})^2}\\\\ f'(t)=\frac{4+2\sqrt{t}-\sqrt{t}}{(2+\sqrt{t})^2}\\\\ \large\boxed{f'(t)=\frac{4+\sqrt{t}}{(2+\sqrt{t})^2}}$