Question

найти производную функцию

у+cos(x-y)=0

Answer 1

$y+\cos(x-y)=0$

Находим производную левой и правой части:

$(y+\cos(x-y))'=0'$

$y'+(-\sin(x-y))\cdot(x-y)'=0$

$y'-\sin(x-y)\cdot(1-y')=0$

$y'-\sin(x-y)+y'\sin(x-y)=0$

Выражаем производную:

$y'+y'\sin(x-y)=\sin(x-y)$

$y'(1+\sin(x-y))=\sin(x-y)$

$y'=\dfrac{\sin(x-y)}{1+\sin(x-y)}$