Question

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

Answer 1

$2x+3y=sinx$
Differentiating both sides w.r.t. $x$, we obtain
$\frac{d}{dx}(2x+3y)=\frac{d}{dx}\left(\sin x\right)$
$\Rightarrow \frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(3y\right)=\cos x$
$\Rightarrow 2+3\frac{dy}{dx}=\cos x$
$\Rightarrow 3\frac{dy}{dx}=\cos x-2$
$\therefore \frac{dy}{dx}=\frac{\cos x-2}{3}$