Question

Determine a derivada :

($(x^{5} - x^{} )/ x^{2}$

Answer 1

$\displaystyle \frac{d}{dx}\left(\frac{x^5-x}{x^2}\right)=\frac{(5x^4-1)x^2-((2x)x^5-x)}{x^4}=\frac{5x^6-x^2-(2x^6-2x^2)}{x^4}\\\\=\frac{3x^6+x^2}{x^4}=\frac{x^2(3x^4+1)}{x^2(x^2)}=\boxed{\frac{3x^4+1}{x^2}}$