Question

Найти производную y= (cosx)/(sin^2 x) * ln tg x

Answer 1

$y= frac{cosx}{sin^2x}cdot ln, tgx\\y'= frac{-sinxcdot sin^2x-cosxcdot 2sinxcdot cosx}{sin^4x} cdot ln, tgx+ frac{cosx}{sin^2x} cdot frac{1}{tgx}cdot frac{1}{cos^2x}=\\= frac{-sin^2x-2cos^2x}{sin^3x} cdot ln, tgx+ frac{1}{sin^3x} = frac{1-ln, tgx(sin^2x+2cos^2x)}{sin^3x}$