# Derivative x^(lnx)

1. Dec 10, 2006

### Fusilli_Jerry89

1. The problem statement, all variables and given/known data
y=x^(lnx) i know the derivative of lnx is 1/x but what about x^(lnx)?

ln(cos-¹x)

2. Relevant equations
N/A

3. The attempt at a solution

ln(cos-¹x) (1/(cos-¹x))(-x/√(1-x²)) -x/(cos-¹x√(1-x²))
The back in the book has the same answer except the -x is a -1 instead.

2. Dec 11, 2006

### neutrino

Where did the cos-1x come from?

Usually, when you want to differentiate a function of the form f(x)^g(x), it helps to take the logarithm of the function and then find the derivative.

y = x^ln(x)

ln(y) = ln(x^ln(x))...
Can you do it from here?

3. Dec 11, 2006

### Fusilli_Jerry89

on the ln(cos^-1x) is a different question.

4. Dec 11, 2006

### neutrino

Oh, okay. There is a -1 because the derivative of arccos(x) is -1/sqrt(1-x^2).

5. Dec 11, 2006

### Fusilli_Jerry89

k I got the first one but i dont get the second one.(ln(cos-¹x))

6. Dec 11, 2006

### Fusilli_Jerry89

k nm I got it thx