# How do you find the derivative of f(x)=3sqrt(x)-(2/sqrt(x))?

Jun 29, 2016

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

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