Question

ln(x+sqrt(x^2+1) найти производную

Answer 1

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