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If $2 \mathrm{x}^{3}-3 \mathrm{y}^{2}=7$, what is $\frac{\mathrm{dy}}{\mathrm{dx}}$ equal to $(\mathrm{y} \neq 0)?$
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The correct answer is:
$\frac{\mathrm{x}^{2}}{\mathrm{y}}$
Let $2 x^{3}-3 y^{2}=7$
Differentiate both side, w.r.t. 'x'
$6 x^{2}-6 y \frac{d y}{d x}=0$
$\Rightarrow \frac{d y}{d x}=\frac{x^{2}}{y}$
Differentiate both side, w.r.t. 'x'
$6 x^{2}-6 y \frac{d y}{d x}=0$
$\Rightarrow \frac{d y}{d x}=\frac{x^{2}}{y}$
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