what is the slope of the function defined as x^x
2006-10-12 13:34:30 · 6 answers · asked by Ralph 101 1 in Science & Mathematics ➔ Mathematics
the slope of the function means the derivative of it
2006-10-12 13:38:40 · update #1
the question asks for the answer not how to set it up. So a someone had said you would need to change x^x to e^(ln(x))x and take the derivative of this (ln(x)+1)x^x the problem has nothing to do with linear slope because this is the slope of a curve
2006-10-13 14:18:34 · answer #1 · answered by acme0072004 1 · 0⤊ 0⤋
Slope is dy/dx (dy means "delta y", the change in y). For a line this is a constant value, if you choose any 2 points on the line you get the same slope. For any other function you do not.
For the function x^x, you can rewrite it as (e^(ln(x)))^x , replacing the first x with "e to the natural log of x". This equals e^(ln(x)*x), which is a simple exponential function you can take the derivative of:
derivative of e^f(x): f'(x)e^f(x)
2006-10-12 13:45:46 · answer #2 · answered by sofarsogood 5 · 0⤊ 0⤋
the gradient, or slope is whatever x is, squared. so if x=2 then slope =4. if x=6 then slope =36 etc .
2006-10-12 13:36:38 · answer #3 · answered by pablovp 1 · 0⤊ 0⤋
Do u know the slope formula? If u don't its y1-y2 over x1-x2.U should go to algbra online. It help me a lot.
2006-10-12 13:54:48 · answer #4 · answered by Tee-Tee 2 · 0⤊ 0⤋
for f(x)=x^2 the slope is f'(x)=2x
2006-10-12 15:18:00 · answer #5 · answered by yupchagee 7 · 0⤊ 0⤋
x^(x-1)
2006-10-12 13:48:27 · answer #6 · answered by Allen Montgomery 2 · 0⤊ 0⤋