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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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