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

Unless told that I must use the chain rule, I would not. But see below.

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To differentiate (2^{2x}), you can use the chain rule. First, take the derivative of the exponent, which is (2x), then multiply by the derivative of the base, which is (2^x) times the natural logarithm of 2 ((2^x \cdot \ln(2))). So the differentiation of (2^{2x}) is (2^{2x} \cdot \ln(2) \cdot 2). Thus, the derivative is (4^x \cdot \ln(2)).

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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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