# How do you find #(dy)/(dx)# given #2xy+y^2=x+y#?

Use product rule and finish it off to get:

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To find (dy)/(dx) given the equation 2xy + y^2 = x + y, differentiate both sides of the equation with respect to x, then solve for (dy)/(dx). After differentiation and rearrangement, the expression for (dy)/(dx) will be obtained. The process involves applying implicit differentiation and algebraic manipulation to isolate (dy)/(dx) on one side of the equation.

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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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