In this interactive figure, exponential functions of the form [math]f\left(x\right)=b^x[/math] are graphed. Drag the slider to change the value of the base, [math]b[/math]. [br][br]Play with the interactive figure to get a sense of the derivative [math]f'\left(x\right)[/math]. You'll observe that [math]f'\left(x\right)[/math] is very similar to [math]f\left(x\right)[/math]. In fact, [math]f'\left(x\right)[/math] is a constant multiple of [math]f\left(x\right)[/math]; [math]f'\left(x\right)=c\cdot f\left(x\right)[/math]. How is that constant [math]c[/math] determined?[br][br]Also, is there a base [math]b[/math] for which [math]f'\left(x\right)=f\left(x\right)[/math]?