$\displaystyle ln(\frac{x}{e^x ln(x)})$

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- Apr 17th 2012, 10:45 PMrabert1completely expand the ln function, then find the derivative
$\displaystyle ln(\frac{x}{e^x ln(x)})$

- Apr 17th 2012, 10:59 PMbiffboyRe: 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 AMHallsofIvyRe: completely expand the ln function, then find the derivative