Question:
Find $\frac{d y}{d x}$ :
$2 x+3 y=\sin y$
Solution:
The given relationship is
Differentiating this relationship with respect to x, we obtain
$\frac{d}{d x}(2 x)+\frac{d}{d x}(3 y)=\frac{d}{d x}(\sin y)$
$\Rightarrow 2+3 \frac{d y}{d x}=\cos y \frac{d y}{d x} \quad$ [By using chain rule]
$\Rightarrow 2=(\cos y-3) \frac{d y}{d x}$
$\therefore \frac{d y}{d x}=\frac{2}{\cos y-3}$
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