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October 16th, 2010, 06:30 AM   #1
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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.
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October 16th, 2010, 07:29 AM   #2
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Re: Derivative problem

Hello, azelio!

Quote:
There is a polynomial with infinite terms which corresponds exactly to:[color=beige] .[/color]

This particular function is its own derivative.
Guided by this fact, find the five first terms of this polynomial.

Hint: the first term is 1.








[color=beige]. . [/color]







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October 17th, 2010, 05:24 PM   #3
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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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