Proving the Derivative of e^x Is e^x
Date: 02/20/2006 at 00:17:22 From: Ethan Subject: Derivation of e^x is e^x What is the delta x proof of (dy/dx)e^x = e^x? I know using delta x you can prove (dx/dy) of x^3 = 3x^2 but I can't work out e^x.
Date: 02/20/2006 at 09:06:43 From: Doctor George Subject: Re: Derivation of e^x is e^x Hi Ethan, Thanks for writing to Doctor Math. Here is a proof that uses the definition of derivative, as you are attempting to do. Proving That d(e^x)/dx = e^x http://mathforum.org/library/drmath/view/53731.html Here are two other approaches that may be of interest to you. 1. Apply the chain rule to ln(e^x) = x. 2. Look at the series expansion of e^x. If you take the derivative of each term in the series you will see that the result is just a duplication of the series. Does that make sense? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/
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