# What is the implicit derivative of #3=(1-y)/x^2+xy #?

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To find the implicit derivative of ( 3 = \frac{{1-y}}{{x^2}} + xy ), differentiate both sides of the equation with respect to ( x ) using the product rule and chain rule where necessary.

( \frac{{d}}{{dx}}[3] = 0 )

( \frac{{d}}{{dx}}\left[\frac{{1-y}}{{x^2}}\right] = \frac{{-2(1-y)}}{{x^3}} - \frac{{(1-y)(-2x)}}{{x^4}} )

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

Then, rearrange terms and solve for ( \frac{{dy}}{{dx}} ).

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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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