# How do you differentiate #f(x)=lnx^2+lnx-x# using the sum rule?

Differentiate each term individually to obtain

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To differentiate the function ( f(x) = \ln(x^2) + \ln(x) - x ) using the sum rule, you differentiate each term separately and then add them together. The derivative of ( \ln(x^2) ) with respect to ( x ) is ( \frac{2x}{x^2} ), the derivative of ( \ln(x) ) with respect to ( x ) is ( \frac{1}{x} ), and the derivative of ( -x ) with respect to ( x ) is ( -1 ). So, the derivative of ( f(x) ) is ( \frac{2}{x} + \frac{1}{x} - 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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