Question

$\frac{(x+5)(2x^2-1)}{x}$

Answer 1

$$\begin{gathered} \frac{d}{dx}\left(\frac{\left(x+5\right)\left(2x^2-1\right)}{x}\right) \\ =\frac{d}{dx}\left(\frac{2x^3+10x^2-x-5}{x}\right) \\ =\frac{d}{dx}\left(\frac{2x^3}{x}\right)+\frac{d}{dx}\left(\frac{10x^2}{x}\right)-\frac{d}{dx}\left(\frac{x}{x}\right)-\frac{d}{dx}\left(\frac{5}{x}\right) \\ =2\frac{d}{dx}\left(x^2\right)+10\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(1\right)-5\frac{d}{dx}\left(x^{-1}\right) \\ =2\left(2x\right)+10\left(1\right)-0-5\left(-1\right)x^{-2} \\ =4x+10+\frac{5}{x^2} \end{gathered}$$