Find f^(n)(x) of f(x)=2^x
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Find f^(n)(x) of f(x)=2^x

[From: ] [author: ] [Date: 12-11-06] [Hit: ]
f^(n)(x) = 2^x * (ln 2)^n.I hope this helps!......
I am supposed to find the nth derivative of 2^x. I am not sure where to start because with each time the derivative gets more complicated. Thanks in advance.

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f '(x) = 2^x * ln 2
f ''(x) = (2^x * ln 2) * ln 2 = 2^x * (ln 2)^2
f '''(x) = (2^x * ln 2) * (ln 2)^2 = 2^x * (ln 2)^3.

So, we see that
f^(n)(x) = 2^x * (ln 2)^n.

I hope this helps!
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