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

Answer 1

Emilia Aguilar

#f'(x) = 2^(1+2x)ln 2#

Given: #f(x) = 2^(2x)#

Derivative rule: #(a^u)' = u' a^u ln (a)#

Let #a = 2; " "u = 2x; " "u' = 2#

#f'(x) = 2* 2^(2x) ln 2#

#f'(x) = 2^1 * 2^(2x) ln 2#

Exponents of the same base are added:

#f'(x) = 2^(1+2x) ln 2#

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Answer 2

Christopher Allers

To differentiate (2^{2x}), you can use the chain rule. First, take the derivative of the exponent, which is (2), and then multiply by the original function with the base (2) raised to the original exponent (2x). So, the derivative of (2^{2x}) is (2 \times 2^{2x}), or simply (4 \times 2^x).

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Answer from HIX Tutor

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.