# How do you find the derivative of (6x*sqrtx)+(8/(x^2*sqrtx))?

Apr 2, 2016

$9 \sqrt{x} - \frac{20}{{x}^{3} \cdot \sqrt{x}}$

#### Explanation:

Change the function into a more workable form with laws of indices. Problems like these are often written to look incomprehensible but become straightforward when rearranged.

$6 {x}^{\frac{3}{2}} + 8 {x}^{- \frac{5}{2}}$

Now differentiate in the normal fashion.

$9 {x}^{\frac{1}{2}} - 20 {x}^{- \frac{7}{2}}$
$= 9 \sqrt{x} - \frac{20}{{x}^{3} \cdot \sqrt{x}}$