Question

Найдите производную
y=1/x-5arctg2x

Answer 1

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