Question

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

Answer 1

The given relationship is 2x + 3y = sin x
Differentiating this relationship with respect to x, we obtain
$\frac {d}{dx}$(2x + 3y) = $\frac {d}{dx}$(sin x)

\implies$$\frac {d}{dx}(2x) + $\frac {d}{dx}$(3y) = cos x

$\implies$2 + 3$\frac {dy}{dx}$ = cos x

$\implies$3$\frac {dy}{dx}$ = cos x - 2

∴ $\frac {dy}{dx}$ = $\frac {cos\ x -2}{3}$