- #1

agenttiny200

- 23

- 0

## Homework Statement

Find the derivative of the following function:

(2

^{x})/(e

^{x})

## Homework Equations

f'(a

^{x}) = a

^{x}. lna

f(e

^{x}) = e

^{x}

I already know the answer, but I don't understand how it comes to it. why does the log(2/e) (from below, 'The attempt at a solution' step 3) appear? and why does it turn into {log(2)-1}? from my understanding, it should turn into log(2) - log(e

^{-1})

## The Attempt at a Solution

f(x) = (2

^{x})/(e

^{x})

f(x) = (2/e)

^{x}

f'(x) = {(2/e)

^{x}} . {log(2/e)}

f'(x) = {(2/e)

^{x}} . {log(2)-1}