# How do you find the derivative of 4/sqrt x?

May 25, 2016

-2/x^(3/2)=-2/(sqrt(x^3)

#### Explanation:

Begin by writing $\frac{4}{\sqrt{x}} = \frac{4}{x} ^ \left(\frac{1}{2}\right) = 4 {x}^{- \frac{1}{2}}$

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

$\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}$

$\Rightarrow \frac{d}{\mathrm{dx}} \left(4 {x}^{- \frac{1}{2}}\right) = \left(- \frac{1}{2} \times 4\right) {x}^{- \frac{1}{2} - 1} = - 2 {x}^{- \frac{3}{2}}$

rArrd/dx(4/sqrtx)=-2x^(-3/2)=-2/(sqrt(x^3)