If y^2(2-x)=x^3, then (d y d x )_ (1,1) is equal to - Vidyadip

Question

If $y^2(2-x)=x^3$, then $\left(\frac{d y}{d x}\right)_{(1,1)}$ is equal to

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Answer

$\text {Given, } y^2(2-x)=x^3$
$\Rightarrow y^2=\frac{x^3}{2-x}$
$\Rightarrow 2 y \cdot \frac{d y}{d x}=\frac{(2-x) \times 3 x^2-x^3(-1)}{(2-x)^2}$
$\Rightarrow \frac{d y}{d x}=\frac{6 x^2-2 x^3}{2 y(2-x)^2}$
$\Rightarrow\left(\frac{d y}{d x}\right)_{(1,1)}=\frac{6-2}{2 \times 1}=2$

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