Question

What is the derivative of e^(2x)

Answer 1

Using the chain rule: The derivative of e^u is (e^u)(u').  Notice that e^u is rewritten exactly as is and then multiplied by the derivative of the exponent.  
Let u=2x. So u'=2  
So the derivative of e^u is e^(2x)*2 This can also be written as 2e^(2x).