Question

Can someone show me the steps to this differentiation? \[\frac { d }{ dx } { 2 }^{ x }\]
How should I start with differentiating this?

Answer 1

2^x

Answer 2

Take log on both sides, y=2^x

Answer 3

http://www.youtube.com/watch?v=sSE6_fK3mu0

Answer 4

\[y=2^{x}\]
\[lny=xln2\]
\[[lny]\prime=\ln2\]
\[y'/y=\ln2\]
\[y'=\ln2*y'\]
\[y'=2^{x}*\ln2\]

Answer 5

d/dx e^x : by d/dx ln(x)
Given : d/dx ln(x) = 1/x; Chain Rule; d/dx x = 1.

(1) d/dx ln(e^x) = d/dx x = 1
d/dx ln(e^x) = d/du ln(u) d/dx e^x (Set u=e^x)
= 1/u d/dx e^x = 1/e^x d/dx e^x = 1 (equation 1)
d/dx e^x = e^x

Answer 6

ohh...Thank you!!!

Answer 7

sorry, second to the last line should read y' = ln2 * y