Find the derivative (calculus)?

1 ⤊

What is the derivative of the function F(x)=x^x with respect to x?

I would at first think it would be x*x^(x-1)=x^x, but I don't think it is.

2006-10-05 10:13:12 · 4 answers · asked by fredorgeorgeweasley 4 in Science & Mathematics ➔ Mathematics

let y=x^x
ln y=xlnx
1/y(dy/dx)=x(1/x)+lnx
dy/dx=y*[1+lnx]
=x^x[1+lnx]

2006-10-05 10:19:38 · answer #1 · answered by raj 7 · 1⤊ 0⤋

Actually, I think you're right.

F(x) = X^X, F'(x) = X*X^x-1 = X^(x-1+1) = X^X

Meaning - the function and derivative are the same.

2006-10-05 17:20:23 · answer #2 · answered by MiTTeLMaNiA 2 · 0⤊ 0⤋

d F(x) = 2x dx

2006-10-05 17:15:59 · answer #3 · answered by Answers1 6 · 0⤊ 0⤋

dF/dx = (ln(x) + 1)*x^x

2006-10-05 17:19:04 · answer #4 · answered by nckobra40 3 · 0⤊ 0⤋