Question

Найдите производную
y=1/x-5arctg2x

Answer 1

$LARGE \ y={1over x-5arctg{2x}}\ y=(x-5arctg{2x})^{-1}\ y'=-(x-5arctg{2x})^{-2}cdot(1-5cdot{1over 1+ 4x^2}cdot2)\ y'=-{1-{10over1+4x^2}over (x-5arctg{2x})^2}\ y'={9-4x^2over (1+4x^2 )cdot(x-5arctg{2x})^2}$