# How do you implicitly differentiate #2= e^(xy^2-xy)-y^2x^3+y #?

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# dy/dx = (3x^2y^2-e^(xy^2-xy)(y^2-y))/(e^(xy^2-xy)(2xy-x)-2x^3y+1)#

We have:

And so:

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To implicitly differentiate the equation ( 2 = e^{xy^2-xy} - y^2x^3 + y ), we differentiate both sides of the equation with respect to ( x ) using the chain rule and product rule where necessary.

[ 0 = \frac{d}{dx}(e^{xy^2-xy} - y^2x^3 + y) ]

[ 0 = e^{xy^2-xy} \cdot \frac{d}{dx}(xy^2 - xy) - \frac{d}{dx}(y^2x^3) + \frac{d}{dx}(y) ]

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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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