The derivative of 2x+3y=siny is:

Question

The derivative of $2 x + 3 y = \sin y$ is:

Smart Achievers · Accepted Answer

(3)

Ans. $\frac{2}{c o s y - 3}$

Explanation:

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

On differentiating both sides w.r.t. $x$ , we get

$\frac{d}{d x} (2 x + 3 y) = \frac{d}{d x} (\sin y)$

$\Rightarrow$ $2 + 3 \frac{d y}{d x} = \cos y \frac{d y}{d x}$

$\Rightarrow$ $3 \frac{d y}{d x} - \cos y \frac{d y}{d x} = - 2$

$\Rightarrow$ $(3 - \cos y) \frac{d y}{d x} = - 2$

$\Rightarrow$ $\frac{d y}{d x} = \frac{2}{\cos y - 3}$

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