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

The Sum Rule simply states that you take the derivative of each term and add them together.

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

[ f(x) = \frac{1}{x} + x ] [ f'(x) = \frac{d}{dx}\left(\frac{1}{x}\right) + \frac{d}{dx}(x) ]

Using the power rule for differentiation, (\frac{d}{dx}\left(\frac{1}{x}\right) = -\frac{1}{x^2}) and (\frac{d}{dx}(x) = 1).

Thus,

[ f'(x) = -\frac{1}{x^2} + 1 ]

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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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