Question #3bdb8

1 Answer
Jun 17, 2017

y=x^x*e^-x

Explanation:

e is the inverse operation of ln, which means they undo or cancel each other out. For example, if you have lnx, you can take e^lnx and you are left with x:

I.e.

cancel(e)^(cancel(ln)x)=x

Also, there is a log law and an index law that will help:

alnb=lnb^a

e^(a+b)=e^a*e^b

First, use the log law to simplify:

lny=xlnx-xrArrlny=lnx^x-x

Next, take e^ of each side of the equation:

rArrcancel(e)^(cancel(ln)y)=e^((ln(x^x)-x))

Use the index law to separate the right hand side:

y=e^ln(x^x)*e^-x

rArry=cancel(e)^(cancel(ln)(x^x))*e^-x

rArry=x^x*e^-x