Why the derivatives of exponential functions, lets say, as apposed to polynomials, grow more rapidly than the functions themselves?

i.e.

$$y={e}^{{x}^{2}}\phantom{\rule{0ex}{0ex}}\frac{\mathrm{d}y}{\mathrm{d}x}=2x{e}^{{x}^{2}}$$

I am interested in a verbal explanation.

i.e.

$$y={e}^{{x}^{2}}\phantom{\rule{0ex}{0ex}}\frac{\mathrm{d}y}{\mathrm{d}x}=2x{e}^{{x}^{2}}$$

I am interested in a verbal explanation.