# How can we know that x^x is an exponential function or not without drawing the graphic?

In general, exponential function is defined as $$a\cdot b^x$$, where $$a$$=coefficient, and $$b$$= base.

I only knew that the function is exponential function or not, just by drawing the graphic.

But, how can we guess that the function is exponential function or not, for example how can we know that $$f(x)=x^x$$ is exponential function or not without drawing the graphic?

Thanks

• How does it help to draw a graphic? Do you mean you plot the graph using a logarithmic scale? – TonyK Aug 8 '14 at 17:09

If you differentiate $f(x)=e^{g(x)}=e^{xln(x)}$ you will see, that $g'(x)$ is not a constant. Thus $f(x)=x^x$ is not an exponential function.