Question

d/dx of
ln(x+{sqrt[x^2 - 1]})

Answer 1

I can get it to this, but then get stuck.

\[1+x^(1/2) \div x+\sqrt{x^2-1}\]

Answer 2

?? What is that?

One piece at a time: \(\dfrac{1}{x+\sqrt{x^{2}-1}}\cdot \left(1 + \dfrac{2x}{2\sqrt{x^{2}-1}}\right)\).

Clearly, there's at least one way to simplify that a little.