# How do you differentiate #f(x)=ln2^x-2lnx #?

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To differentiate ( f(x) = \ln(2^x) - 2\ln(x) ), you would use the chain rule and the power rule for logarithmic functions. The derivative is ( f'(x) = \frac{d}{dx}[\ln(2^x)] - \frac{d}{dx}[2\ln(x)] ). Applying the rules, the derivative is ( f'(x) = \frac{1}{2^x} \cdot \ln(2) - \frac{2}{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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