# How do you find #dy/dx# by implicit differentiation of #sqrt(xy)=x-2y#?

This is a homogeneous equation and no need for implicit differentiation.

so

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To find (\frac{{dy}}{{dx}}) by implicit differentiation of (\sqrt{xy} = x - 2y), follow these steps:

- Differentiate both sides of the equation with respect to (x).
- Apply the chain rule where necessary.
- Solve the resulting equation for (\frac{{dy}}{{dx}}).

The derivative of the equation (\sqrt{xy} = x - 2y) with respect to (x) yields:

[ \frac{1}{2\sqrt{xy}}(y + xy') = 1 - 2y']

Solve for (\frac{{dy}}{{dx}}):

[y' = \frac{{2\sqrt{xy} - y}}{{4x - 2y}}]

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