# How do you differentiate #y=e^-x/x#?

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To differentiate ( y = \frac{e^{-x}}{x} ), use the quotient rule:

[ \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{u'v - uv'}{v^2} ]

Here, ( u = e^{-x} ) and ( v = x ).

Find the derivatives: [ u' = -e^{-x} ] [ v' = 1 ]

Apply the quotient rule: [ \frac{d}{dx} \left( \frac{e^{-x}}{x} \right) = \frac{-e^{-x} \cdot x - e^{-x} \cdot 1}{x^2} ] [ = \frac{-xe^{-x} - e^{-x}}{x^2} ]

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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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