# How do you find the derivative of y = (x^2 + sqrtx + 1 ) / x^(3/2)?

Dec 16, 2017

$y ' = \frac{1}{2 {x}^{\frac{1}{2}}} - \frac{1}{x} ^ 2 - \frac{3}{2 {x}^{\frac{5}{2}}}$

#### Explanation:

Start by simplifying:

$y = {x}^{2 - \frac{3}{2}} + {x}^{\frac{1}{2} - \frac{3}{2}} + {x}^{0 - \frac{3}{2}}$

$y = {x}^{\frac{1}{2}} + {x}^{- \frac{2}{2}} + {x}^{- \frac{3}{2}}$

$y = {x}^{\frac{1}{2}} + {x}^{- 1} + {x}^{- \frac{3}{2}}$

$y ' = \frac{1}{2} {x}^{- \frac{1}{2}} - {x}^{- 2} - \frac{3}{2} {x}^{- \frac{5}{2}}$

$y ' = \frac{1}{2 {x}^{\frac{1}{2}}} - \frac{1}{x} ^ 2 - \frac{3}{2 {x}^{\frac{5}{2}}}$

Hopefully this helps!