# completely expand the ln function, then find the derivative

• Apr 17th 2012, 10:45 PM
rabert1
completely expand the ln function, then find the derivative
$ln(\frac{x}{e^x ln(x)})$
• Apr 17th 2012, 10:59 PM
biffboy
Re: completely expand the ln function, then find the derivative
Expression= lnx-ln(e^xlnx)=lnx-(lne^x+ln(lnx)=lnx-x-ln(lnx)

Derivative=1/x-1-1/(xlnx) (The last term came from 1/lnx times 1/x by the chain rule)
• Apr 18th 2012, 06:41 AM
HallsofIvy
Re: completely expand the ln function, then find the derivative
Quote:

Originally Posted by rabert1
$ln(\frac{x}{e^x ln(x)})$

Are you saying that you do not know the "laws of logarithms"? It seems strange that you would be taking a course that asked you find derivatives of logarithm functions if you have never taken a course that dealt with logarithms.