Hi Claudia,
I'll do the second problem for you to give you an idea how to approach the third problem.
Let
z = x^{ln(x)}
Take the natural log of both sides and use the property that ln(a^{b}) = b ln(a).
ln(z) = ln(x^{ln(x)}) = ln(x) ln(x) = [ln(x)]^{2}
Now differentiate to get
^{z'}/_{z} = 2 [ln(x)] ^{1}/_{x}
Thus
z' = z 2 [ln(x)] ^{1}/_{x} = 2 x^{ln(x)} ^{ln(x)}/_{x}
Apply the same technique to the third problem. For the first problem the first step is to use the property of the log that I used above.
Penny
