# How do you find the derivative of y =4/sqrt(x)?

Aug 2, 2014

When you're differentiating things involving radicals, it's never a bad idea to rewrite the radicals as rational exponents:

$y = 4 {x}^{- \frac{1}{2}}$

Now, this is easily differentiated using the power rule:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(- \frac{1}{2}\right) \cdot 4 {x}^{- \frac{3}{2}}$

Simplified:

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

And, if we want to put the answer in radical form:

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