## xEnOnn 3 years ago Can someone show me the steps to this differentiation? $\frac { d }{ dx } { 2 }^{ x }$ How should I start with differentiating this?

1. .Sam.

2^x

2. arcticf0x

Take log on both sides, y=2^x

3. .Sam.
4. dpaInc

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

5. .Sam.

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

6. xEnOnn

ohh...Thank you!!!

7. dpaInc

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