# How do you find the derivative of y=(9x^2+1)/(x^2+7)?

Dec 15, 2015

Simplify, then use the power rule and chain rule to find:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{124 x}{{x}^{2} + 7} ^ 2$

#### Explanation:

First simplify:

$y = \frac{9 {x}^{2} + 1}{{x}^{2} + 7} = \frac{9 \left({x}^{2} + 7\right) - 62}{{x}^{2} + 7} = 9 - 62 {\left({x}^{2} + 7\right)}^{- 1}$

Then use the power rule and chain rule to find:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x \cdot 62 {\left({x}^{2} + 7\right)}^{-} 2 = \frac{124 x}{{x}^{2} + 7} ^ 2$