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

Take natural logs of both sides:

Implicitly differentiate both sides:

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To differentiate the function ( f(x) = 2^x ), you would use the chain rule. The derivative of ( 2^x ) with respect to ( x ) is ( \ln(2) \times 2^x ). So, the derivative of ( f(x) ) is ( f'(x) = \ln(2) \times 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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