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?

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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?

MIT 18.01 Single Variable Calculus (OCW)
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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.
Thanks a lot!

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