If 2x+3y=sinx, then dy/dx is equal to:

Question

If $2 x + 3 y = \sin x$ , then $\frac{d y}{d x}$ is equal to:

Smart Achievers · Accepted Answer

(2)

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

Explanation:

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

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

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

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

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

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

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