Question

DERIVADA DE  f(x)= x.√x + 1/x²

Answer 1

Regra do tombo

$\boxed{f(x) = x^n\rightarrow\ f'(x) = n*x^{n-1}}$

Temos que:

$f(x) = x\sqrt{x}+\frac{1}{x^2}\\\\ f(x) = x*x^{\frac{1}{2}}+x^{-2}\\\\ f(x) = x^{\frac{3}{2}}+x^{-2}$

$f'(x) =\frac{3}{2}* x^{\frac{3}{2}-1}+-2*x^{-2-1}\\\\ f'(x)=\frac{3}{2}* x^{\frac{1}{2}}+-2*x^{-3}\\\\ \boxed{f'(x)=\frac{3}{2}*\sqrt{x}-\frac{2}{x^3}}$