# How do you differentiate y=(v^3-2vsqrtv)/(v)?

Mar 4, 2017

$2 v - \frac{1}{\sqrt{v}}$

#### Explanation:

Both terms on top have a $v$ in them, which is the denominator too, so you can actually rewrite quite simply:

$\frac{{v}^{3} - 2 v \sqrt{v}}{v} = {v}^{2} - 2 \sqrt{v} = {v}^{2} - 2 {v}^{\frac{1}{2}}$

Now we have a simple situation of using the power rule, where

$\frac{d}{\mathrm{dx}} a {x}^{n} = n \cdot a {x}^{n - 1}$

so, in the case above,

$\frac{d}{\mathrm{dx}} \left[{v}^{2} - 2 {v}^{\frac{1}{2}}\right] = 2 v - \frac{1}{2} \cdot 2 {v}^{\frac{1}{2} - 1}$

$= 2 v - {v}^{- \frac{1}{2}}$

$= 2 v - \frac{1}{\sqrt{v}}$