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

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Simplify then differentiate to find:

#(dy)/(dx) = 2x-1# when#y != 0#

Multiply by

#(dy)/(dx) = ((2x-1)y)/(x^2-x-1)#

graph{y=x^2y-y^2-xy [-10, 10, -5, 5]}

We can rearrange this as:

Hence:

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To differentiate y=x^2y-y^2-xy, you would use the product rule and the chain rule. The derivative with respect to x is:

dy/dx = 2xy + x^2(dy/dx) - 2y(dy/dx) - y^2 - x(dy/dx)

Then, you would solve for (dy/dx) to find the derivative of y with respect to 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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