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# Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: x$

$\begin{array}{1 1} \frac{cosx-2}{3} \\ \large \frac{cosx+2}{3} \\ \large \frac{sinx-2}{3} \\ \large \frac{sinx+2}{3} \end{array}$

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## 1 Answer

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Toolbox:
• For equations that are not of the form $y = f(x)$, we need to differentiate each term separately on LHS and RHS and then calculate $\large \frac{dy}{dx}$
Given $2x +3y = sin \: x$:
This is not a standard differentiation of the form $y = f(x)$. We need to differentiate each term separately on LHS and RHS and then calculate $\large \frac{dy}{dx}$
Differentiating both sides, $\rightarrow 2\; dx + 3\; dy = cosx\; dx$
$\Rightarrow 3\;dy = dx\; (cosx - 2)$
$\Rightarrow \large \frac{dy}{dx} = \frac{cosx-2}{3}$
answered Apr 5, 2013

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