# How do you find the derivative of y = (x^2+4x+3)/x^.5?

Jul 11, 2015

If this is $y = \frac{{x}^{2} + 4 x + 3}{x} ^ 0.5$, we can use the quotient rule or rewrite as follows.

#### Explanation:

$y = \frac{{x}^{2} + 4 x + 3}{x} ^ 0.5 = {x}^{2} / {x}^{0.5} + \frac{4 x}{x} ^ 0.5 + \frac{3}{x} ^ 0.5$

$= {x}^{1.5} + 4 {x}^{0.5} + 3 {x}^{-} 0.5$

So

$y ' = 1.5 {x}^{0.5} + 2 {x}^{-} 0.5 + 1.5 {x}^{-} 1.5$