Question

Найти производную ln(x+√(1+x^2))

Answer 1

$(ln(x+ sqrt{1+x^2})'= frac{1}{x+ sqrt{1+x^2} }*(x+ sqrt{1+x^2})'= \= frac{1}{x+ sqrt{1+x^2} }*(1+ frac{1}{2 sqrt{1+x^2} }*(1+x^2)')= frac{1}{x+ sqrt{1+x^2} }* (1+frac{2x }{2 sqrt{1+x^2} })= \ = frac{sqrt{1+x^2}+x }{(x+ sqrt{1+x^2}) sqrt{1+x^2} }= frac{1}{ sqrt{1+x^2} }$