$F i n d \frac{d y}{d x} i n t h e f o l l o w i n g :$
1) $2 x + 3 y = sin x$
2) $a x + b y^{2} = cos x$
3) $x^{3} + x y + y = 100$

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Solution

1) $2 x + 3 y = sin x$

Differentiating w.r.t $x$ :
$2 + 3 \frac{d y}{d x} = cos x$

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

2) $a x + b y^{2} = cos x$

Differentiating w.r.t $x$ :
$a + 2 b y \frac{d y}{d x} = - sin x$

$\Rightarrow \frac{d y}{d x} = \frac{- sin x - a}{2 b y}$

3) $x^{3} + x y + y = 100$

Differentiating w.r.t $x$ :
$3 x^{2} + x y^{'} + y = 0$

$\Rightarrow y^{'} = \frac{- y - 3 x^{2}}{x}$

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