Question

If $\cos y=x\cos (a+y)$, find $\frac{dy}{dx}$.

Answer 1

cosy=x cos (a+y)

on differentiating wrt x we get

$\frac{d}{dx}\left(cosy\right)=\frac{d}{dx}\left[xcos\right(a+y\left)\right]$

$-siny\frac{dy}{dx}=cos(a+y)+x(-sin(a+y\left)\right)\frac{dy}{dx}$

$\frac{dy}{dx}\left[xsin\right(a+y)-siny]=cos(a+y)$

$\frac{dy}{dx}=\frac{cos(a+b)}{xsin(a+y)-siny}$