# How do you differentiate y= (sqrt(x)+x) / x^2?

May 10, 2016

$- \left(\frac{3}{2 {x}^{\frac{5}{2}}} + \frac{1}{x} ^ 2\right)$

#### Explanation:

divide terms on numerator by ${x}^{2}$

$\Rightarrow y = {x}^{\frac{1}{2}} / {x}^{2} + \frac{x}{x} ^ 2 = {x}^{- \frac{3}{2}} + {x}^{-} 1$

now differentiate each term using the $\textcolor{b l u e}{\text{ power rule }}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{3}{2} {x}^{- \frac{5}{2}} - 1 {x}^{-} 2$

and writing with positive indices gives.

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \left(\frac{3}{2 {x}^{\frac{5}{2}}} + \frac{1}{x} ^ 2\right)$