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

Question

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

.sam. · Answer

2^x

anonymous · Answer

Take log on both sides, y=2^x

.sam. · Answer

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

anonymous · Answer

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

.sam. · Answer

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

anonymous · Answer

ohh...Thank you!!!

anonymous · Answer

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