# How do you differentiate #f(x)= e^x/(e^(-x) -x )# using the quotient rule?

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To differentiate ( f(x) = \frac{e^x}{e^{-x} - x} ) using the quotient rule:

- Apply the quotient rule: ( \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{u'v - uv'}{v^2} ).
- Let ( u = e^x ) and ( v = e^{-x} - x ).
- Find the derivatives: ( u' = e^x ) and ( v' = -e^{-x} - 1 ).
- Substitute the derivatives and functions into the quotient rule formula.
- Simplify the expression if possible.

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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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