Question

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

Answer 1

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

`(dy)/(dx) = (124x)/(x^2+7)^2`

Explanation:

First simplify:

`y=(9x^2+1)/(x^2+7)=(9(x^2+7)-62)/(x^2+7)=9-62(x^2+7)^(-1)`

Then use the power rule and chain rule to find:

`(dy)/(dx) = 2x*62(x^2+7)^-2 = (124x)/(x^2+7)^2`