# What is the derivative of 5/sqrtx?

Jan 12, 2017

I got: $f ' \left(x\right) = - \frac{5}{2 x \sqrt{x}}$

#### Explanation:

We can use the fact that $\frac{1}{\sqrt{x}} = {x}^{- \frac{1}{2}}$ and derive as usual as an exponent:
$f ' \left(x\right) = 5 \cdot - \frac{1}{2} \cdot {x}^{- \frac{1}{2} - 1} = - \frac{5}{2} {x}^{- \frac{3}{2}} = - \frac{5}{2 {x}^{\frac{3}{2}}} = - \frac{5}{2 x \sqrt{x}}$

Jan 12, 2017

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

#### Explanation:

$\frac{d}{\mathrm{dx}} \frac{5}{\sqrt{x}} = \frac{d}{\mathrm{dx}} 5 {x}^{- \frac{1}{2}}$

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

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