Tricky (for me anyway) Differentiation.

Hi

I am trying to differentiate.

Many attempts at trying, and I cannot get to the answer. I am doing something wrong. Just having the answer is not helping. I have tried using the product and quotient rule(s) but am probably not simplifying correctly. If someone can show the steps that would really be great.

$\displaystyle \frac{x^2-1}{\sqrt{x^2+1}}$

Thanks

Regards

Craig.

Tricky (for me anyway) Differentiation

Here are some steps.

Here is the start.

$\displaystyle

\frac{2x.\sqrt{x^2+1}+\frac{x.\sqrt{x^2+1}}{(x^2+1 )^2}.(x^2-1)}{(x^2+1)}

$

Then

$\displaystyle

\frac{(x.\sqrt{x^2+1}).(2(x^2+1)^2+(x^2-1))}{(x^2+1)^3}

$

But something is wrong. I need to get to:

$\displaystyle

\frac{x.(x^2+3).\sqrt{x^2+1}}{(x^2+1)^2}

$

I cannot see how simplifying will get the terms I need to cancel.

Cannot seem to get there. I have pages of working, and I am doing something stupid.