By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
How to use logarithmic differentiation
Logarithmic differentiation is a combination of derivative rules and logarithm properties which is useful to derive power, exponential and power-exponential functions:
y = 2ˣ
㏑ y = ㏑ 2ˣ
㏑ y = x ㏑ 2
y' / y = ㏑ 2
y' = y · ㏑ 2
y' = 2ˣ · ㏑ 2
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
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