# How do you find the derivative of f(x)=(8x+3)^.5?

Mar 1, 2017

$f ' \left(x\right) = \frac{4}{\sqrt{8 x + 3}}$

#### Explanation:

We have:

$f \left(x\right) = {\left(8 x + 3\right)}^{.5} \left(= \sqrt{8 x + 3}\right)$

Applying the power rule we have:

$f ' \left(x\right) = \frac{1}{2} {\left(8 x + 3\right)}^{- \frac{1}{2}} \left(8\right)$
$\text{ } = 4 {\left(8 x + 3\right)}^{- \frac{1}{2}}$
$\text{ } = \frac{4}{\sqrt{8 x + 3}}$