If x2-y2+3x=5y then dydx=

1 - y 2 - 1 - x 2 1 - y 2 1 - x 2 - 1 - x 2 1 - y 2

Q.

If $x^{2} - y^{2} + 3 x = 5 y$ then $\frac{dy}{dx} =$

Easy

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$\frac{\sqrt{y} (4 x \sqrt{x} - \sqrt{y})}{\sqrt{x} (2 \sqrt{y} + \sqrt{x})}$

$\frac{\sqrt{y} (1 - 2 \sqrt{xy} - y)}{\sqrt{x} (1 + 2 \sqrt{xy} + x)}$

$\frac{2 x + 3}{2 y + 5}$

$\frac{\sqrt{1 - y^{2}} - \sqrt{(1 - x^{2}) (1 - y^{2})}}{\sqrt{1 - x^{2}} - \sqrt{(1 - x^{2}) (1 - y^{2})}}$

answer is C.

(Detailed Solution Below)

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Detailed Solution

The given equation is $x^{2} - y^{2} + 3 x = 5 y$

Use implicit differentiation, differentiate both sides with respect to $x$

$\begin{array}{rcl} 2 x - 2 y \frac{d y}{d x} + 3 & = & 5 \frac{d y}{d x} \\ \frac{d y}{d x} (2 y + 5) & = & 2 x + 3 \\ \frac{d y}{d x} & = & \frac{2 x + 3}{2 y + 5} \end{array}$

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