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:

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

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