Finding the derivative of x^(lnx) and ln(arccos(x))

[Fusilli_Jerry89]

Homework Statement

y=x^(lnx) i know the derivative of lnx is 1/x but what about x^(lnx)?

ln(cos-¹x)

Homework Equations

N/A

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.

 

[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?

 

[Fusilli_Jerry89]

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

 

[neutrino]

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

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

 

[Fusilli_Jerry89]

k I got the first one but i don't get the second one.(ln(cos-¹x))

 

[Fusilli_Jerry89]

k nm I got it thx