Math 105-02: Calculus I: Reading Homework 4.2

1. The Exponential Function : what general argument does the book use to come up with an idea of what the derivative of the exponential function must look like?
   
   1. The Derivative of a^x :
      
      1. 2^x : how does the book find the derivative of 2^x? what is the formula that it obtains?
         
      2. a^x : how does the book define e? what are the resulting formulas that it obtains for the derivatives of a^x and e^x?