Find frac{dy}{dx} for the equation 2x + 3y = | vedclass

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(A) Given the equation: $2x + 3y = \sin x$. Differentiating both sides with respect to $x$: $\frac{d}{dx}(2x + 3y) = \frac{d}{dx}(\sin x)$ Applying th

Vedclass · Accepted Answer

$\frac{\cos x - 2}{3}$

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(A) Given the equation: $2x + 3y = \sin x$. Differentiating both sides with respect to $x$: $\frac{d}{dx}(2x + 3y) = \frac{d}{dx}(\sin x)$ Applying the sum rule and derivative rules: $\frac{d}{dx}(2x) + \frac{d}{dx}(3y) = \cos x$ $2 + 3 \frac{dy}{dx} = \cos x$ Subtracting $2$ from both sides: $3 \frac{dy}{dx} = \cos x - 2$ Dividing by $3$: $\frac{dy}{dx} = \frac{\cos x - 2}{3}$

Find $\frac{dy}{dx}$ for the equation $2x + 3y = \sin x$.

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