# How do you differentiate #f(x)=3/x-5/(1-x)# using the sum rule?

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To differentiate ( f(x) = \frac{3}{x} - \frac{5}{1-x} ) using the sum rule, you differentiate each term separately and then sum the results.

( f(x) = \frac{3}{x} - \frac{5}{1-x} )

First term: ( \frac{3}{x} ) Using the power rule, the derivative is ( -\frac{3}{x^2} ).

Second term: ( -\frac{5}{1-x} ) Using the chain rule, the derivative is ( -\frac{5}{(1-x)^2} ).

Summing the derivatives of each term, we get:

( f'(x) = -\frac{3}{x^2} - \frac{5}{(1-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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