# How do you use the power rule to differentiate f(x)=3x^5+2/sqrtx?

Nov 22, 2016

$f ' \left(x\right) = 15 {x}^{4} - \frac{1}{x} ^ \left(\frac{3}{2}\right)$

#### Explanation:

We can rewrite the equation so we can apply the power rule.

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

Then when we differentiate using the power rule:

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

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