Question

Encontre a derivada de y= 1/x ∗ (x^2+1/x)

A)y′= 1 − 2/x^3
B)y′= 2 − 3/x^3
C)y′= 1 + 2/x^3
D)y′= 1 − 2/x^2
E)y′= 2/x^3

Answer 1

$\displaystyle \sf y=\frac{1}{x}\cdot \left(x^2+\frac{1}{x}\right) \\\\\\ y = x+\frac{1}{x^2} \\\\\\ y = x+x^{-2} \\\\ Derivando : \\\\\ y'=(x) '+(x^{-2})' \\\\ y' = 1+(-2\cdot x^{-3}) \\\\ \huge\boxed{\sf \ y'=1-\frac{2}{x^3}\ }\checkmark$

item A