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

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Answer 1 · 2018-06-21T05:25:42

#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#