We have, #10; #10; 2x+3y=sin x #10; #10;On differentiating and we get, #10; #10; ddx( 2x+3y )=ddxsin x #10; #10; ⇒ 2dxdx+3dydx=cos ...

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Parametric Differentiation

2x+3y=sinx fi...

Question

$2 x + 3 y = s i n x$ find $\frac{d y}{d x}$

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Solution

We have,

$2 x + 3 y = sin x$

On differentiating and we get,

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

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

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

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

Hence, this is the answer.

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