How do you differentiate 2^(2x)?

Jun 21, 2018

$f ' \left(x\right) = {2}^{1 + 2 x} \ln 2$

Explanation:

Given: $f \left(x\right) = {2}^{2 x}$

Derivative rule: $\left({a}^{u}\right) ' = u ' {a}^{u} \ln \left(a\right)$

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

$f ' \left(x\right) = 2 \cdot {2}^{2 x} \ln 2$

$f ' \left(x\right) = {2}^{1} \cdot {2}^{2 x} \ln 2$

Exponents of the same base are added:

$f ' \left(x\right) = {2}^{1 + 2 x} \ln 2$