What is the derivative of 2^x?

2 Answers
Rajat Chatterjee
Nov 5, 2016

#2^xln2#.

Explanation:

we know #d/dx a^x=a^x lna#.so the ans.

George C.
Nov 5, 2016

#d/(dx) 2^x = 2^x*ln 2#

Explanation:

By the definition of natural logarithm:

#e^(ln 2) = 2#

So:

#2^x = (e^(ln 2))^x = e^(x ln 2)#

Given that:

#d/(dx) e^x = e^x#

we can use the chain rule to deduce:

#d/(dx) 2^x = d/(dx) e^(x ln 2)#

#color(white)(d/(dx) 2^x) = e^(x ln 2) * d/(dx) (x ln 2)#

#color(white)(d/(dx) 2^x) = e^(x ln 2) * ln 2#

#color(white)(d/(dx) 2^x) = 2^x * ln 2#

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