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

Find the derivative of each individual part using the power rule:

Thus,

This can also be written as:

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

So, for the first term, ( \frac{1}{x} ), the derivative is ( -\frac{1}{x^2} ).

For the second term, ( \frac{1}{x^3} ), the derivative is ( -\frac{3}{x^4} ).

Adding these derivatives together, you get:

( f'(x) = -\frac{1}{x^2} - \frac{3}{x^4} ).

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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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