Question

Find $\frac{dy}{dx}$ of $2x+3y=\sin y$

Answer 1

Given, $2x+3y=\sin y$

Differentiating both sides respect to x, we get,

$\Rightarrow \frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(3y\right)=\frac{d}{dx}\left(\sin y\right)$

$\Rightarrow 2+3\frac{dy}{dx}=\cos y\frac{dy}{dx}$

$\Rightarrow 2=(\cos y-3)\frac{dy}{dx}$

$\therefore \frac{dy}{dx}=\frac{2}{\cos y-3}$