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Algebra of Derivatives

If 32+y3=3a...

Question

If $\frac{3}{2} + y^{3} = 3 a x y$ , then find $\frac{d y}{d x}$

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Solution

$\frac{3}{2} + y^{3} = 3 a x y$
On differentiating we get,
$3 y^{2} \frac{d y}{d x} = 3 a y + 3 a x \frac{d y}{d x}$
$⟹ \frac{d y}{d x} = \frac{3 a y}{3 y^{2} - 3 a x}$
$⟹ \frac{d y}{d x} = \frac{a y}{y^{2} - a x}$

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