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How do you implicitly differentiate #-1=y^2+(x-e^y)/(x)#?

Answer 1

Isabella Ackerman

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Answer 2

Emma Aldridge

To implicitly differentiate -1=y^2+(x-e^y)/(x), first, differentiate each term with respect to x, then apply the chain rule when necessary:

d/dx(-1) = 0 d/dx(y^2) = 2y(dy/dx) d/dx((x-e^y)/(x)) = [(x)(1) - (x-e^y)(1/x)] / x^2

So, the implicit differentiation yields:

0 = 2y(dy/dx) + [(x - e^y) - (x-e^y)/x] / x^2

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Answer from HIX Tutor

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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