Name of this math function?
f(x) = x^x
Is it exponential (f(x) = 2^x) or ar power (f(x)= x^2)) function, or neither?
f(x) = x^x
Is it exponential (f(x) = 2^x) or ar power (f(x)= x^2)) function, or neither?
?
There's no common name for that function. It's not used very much in practice--it shows up in calculus homework and the like since it's a good place to use logarithmic differentiation; it shows up in the "sophomore's dream" identity, which is a nice curiosity but I don't know of any applications. Exponential and power functions come up a lot in nature, while x^x doesn't seem to. It probably has an awful differential equation form....
Anonymous
It is both an exponential and power function. f(x) can be written as e^(xlnx), which is an exponential function of xlnx, which in turn is a function of x.