Question

Has anyone watched Pro.Strang's Highlights of Calculus? In the video lecture on Growth Rates and Log Graphs he put down x! Does that mean that x is continuous? And is x^x a function? Would it have a derivative?

Answer 1

I have not seen the video, but x! (x factorial) means x*(x-1)*(x-2)*...*3*2*1
4!=4*3*2*1=24

y=x^x is a function.
If defined for x>0, it will have a derivative. You can go to
http://www.analyzemath.com/calculus/Differentiation/first_derivative.html
for how to do the derivative.

Answer 2

Thanks a lot!