What is the derivative of 2^x?
2 Answers
Nov 5, 2016
Explanation:
we know
Nov 5, 2016
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