Question

Помогите пожалуйста!!!! Срочно
Найти производную от функции, заданной неявно:y sin x=cos(x-y)

Answer 1

y·sinx = cos(x-y)

[y·sinx ]' = [cos(x-y)]'

y'·sinx + y·cosx = -sin(x-y)·(1-y')

y'·sinx + y·cosx = -sin(x-y)+sin(x-y)·y'

sin(x-y)·y' - y'·sinx = y·cosx + sin(x-y)

y'·(sin(x-y) - sinx) = y·cosx + sin(x-y)

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