Question

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

Answer 1

`dy/dx=(4x)/(x^2+1)^2`

Explanation:

We can also rewrite the function:

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

Then, through the chain rule, we see that:

`dy/dx=-2(-(x^2+1)^-2)d/dx(x^2+1)=2/(x^2+1)^2(2x)=(4x)/(x^2+1)^2`