Trouble finding the derivative

[raul_l]

Hi

I'm having trouble finding the derivative of this function.

$$y=x ln (x+\sqrt{1+x^2})-\sqrt{1+x^2}$$

This is what I've tried so far, but I seem to be getting nowhere.

 

[arildno]

Hi raul!
The nasty part of this is, of course the logarithm part, and possibly rearranging the expression you get afterwards.

For starters:
What is the derivative wrt. x of $\sqrt{1+x^{2}}$?

 

[raul_l]

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

 

[arildno]

Why the minus sign??

 

[raul_l]

Right, no minus sign there.. my bad.

However, now I get $$\ln(x+\sqrt{1+x^2})$$
Is this correct?