# How do you differentiate #f(x) = (e^x-4x)/(2x-e^x)# using the quotient rule?

The answer is

The rule of the quotient is

Here,

Consequently,

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To differentiate ( f(x) = \frac{e^x - 4x}{2x - e^x} ) using the quotient rule, follow these steps:

- Let ( u = e^x - 4x ) and ( v = 2x - e^x ).
- Find the derivatives ( u' ) and ( v' ) with respect to ( x ).
- Apply the quotient rule: ( f'(x) = \frac{u'v - uv'}{v^2} ).
- Substitute the values of ( u ), ( v ), ( u' ), and ( v' ) into the formula.
- Simplify the expression to get the derivative of ( f(x) ).

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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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