# How do you find the derivative using the Quotient rule for f(z)= (z^2+1)/(sqrtz)?

Jun 14, 2015

$y ' = \frac{3 {z}^{2} - 1}{2 z \sqrt{z}}$.

#### Explanation:

In this way:

$y ' = \frac{2 z \cdot \sqrt{z} - \left({z}^{2} + 1\right) \cdot \frac{1}{2 \sqrt{z}}}{\sqrt{z}} ^ 2 =$

$= \frac{\frac{2 z \cdot \sqrt{z} \cdot 2 \sqrt{z} - {z}^{2} - 1}{2 \sqrt{z}}}{z} = \frac{4 {z}^{2} - {z}^{2} - 1}{2 z \sqrt{z}} =$

$= \frac{3 {z}^{2} - 1}{2 z \sqrt{z}}$.