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\( (x+y)^{2}=2 a x y \)Find dy/dx. |
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Answer» \((x + y)^2 = 2axy\) Differentiate both sides w.r.t. x, then \(2(x + y) \left(1 + \frac{dy}{dx}\right) = 2a \left(x\frac{dy}{dx} + y\right)\) ⇒ \((2x + 2y - 2ax) \frac{dy}{dx} = 2ay - 2x - 2y\) ⇒ \(\frac{dy}{dx} = \frac{2(ay - y - x)}{2(x + y - ax)} = \frac{y(a -1)-x}{x(1 -a)}\) |
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