Найти производную ln(x+√(1+x^2))

[latex](ln(x+ \sqrt{1+x^2})'= \frac{1}{x+ \sqrt{1+x^2} }*(x+ \sqrt{1+x^2})'= \\= \frac{1}{x+ \sqrt{1+x^2} }*(1+ \frac{1}{2 \sqrt{1+x^2} }*(1+x^2)')= \frac{1}{x+ \sqrt{1+x^2} }* (1+\frac{2x }{2 \sqrt{1+x^2} })= \\ = \frac{\sqrt{1+x^2}+x }{(x+ \sqrt{1+x^2}) \sqrt{1+x^2} }= \frac{1}{ \sqrt{1+x^2} } [/latex]