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October 16th, 2010, 06:30 AM  #1 
Newbie Joined: Oct 2010 Posts: 14 Thanks: 0  Derivative problem
I've never been good with math . Here is the question: There is a polynomial with many(infinite) terms which corresponds exactly this function y=e^x. Guided by this particular function is its own derivative, try to solve the five first terms in this polynomial. Guidence: the first term is 1. I've no idea , thank you. 
October 16th, 2010, 07:29 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Derivative problem Hello, azelio! Quote:
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October 17th, 2010, 05:24 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Derivative problem
Quite interesting... the Maclaurin expansions for sin(x) and cos(x) can be derived similarly by using: y = y'' and for sin(x) begin the polynomial with x, and for cos(x) begin with 1. 

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