# How do you differentiate #x^2+y^2=2xy#?

Saikiran Reddy and Kwasi F. give excellent solutions to this. The answer,

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To differentiate the implicit equation (x^2 + y^2 = 2xy), follow these steps:

- Implicitly differentiate both sides of the equation with respect to (x).
- Use the chain rule and product rule where necessary.
- Solve for (\frac{{dy}}{{dx}}) to find the derivative of (y) with respect to (x).

Differentiating both sides with respect to (x):

[ \frac{{d}}{{dx}}(x^2 + y^2) = \frac{{d}}{{dx}}(2xy) ]

Using the chain rule and product rule:

[ 2x + 2y\frac{{dy}}{{dx}} = 2y + 2x\frac{{dy}}{{dx}} ]

Rearranging terms and solving for (\frac{{dy}}{{dx}}):

[ 2y\frac{{dy}}{{dx}} - 2x\frac{{dy}}{{dx}} = 2x - 2y ] [ \frac{{dy}}{{dx}}(2y - 2x) = 2x - 2y ] [ \frac{{dy}}{{dx}} = \frac{{2x - 2y}}{{2y - 2x}} ]

Simplify:

[ \frac{{dy}}{{dx}} = \frac{{x - y}}{{y - x}} ]

Therefore, the derivative of (y) with respect to (x) for the given implicit equation is (\frac{{x - y}}{{y - x}}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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