how do I find the dirivitive of

Arrummzen · 2004-06-10T10:59:52

I am reading a book called "Elementary Calculus: An Approach Using Infinitesimals" in my spare time. On page 69 there is the problem - y=(x^2+5)^3 How do I solve it? I get the answer 3(x^2+5)^2 yet my calculater says it is 6x(x^2+5)^2. My calculater is correct (I graphed the line and my dirivitive and the calcs dirivitve and the calculater gives a much better answer. My question is, how did it get that answer? Thank you for your time, Arrummzen

Math and Physics Programming

Started by Arrummzen June 09, 2004 05:56 PM

11 comments, last by Arrummzen 19 years, 10 months ago

danielf

122

June 09, 2004 07:40 PM

you have df(g(x))/dx, by definition, is:

lim (f(g(x))-f(g(x0)))/(x-x0)
x->x0

if you multiply the numerator and the denominator by
(g(x)-g(x0), you get:

lim ((f(g(x))-f(g(x0)))*(g(x)-g(x0)))/((x-x0)*(g(x)-g(x0))
x->x0

just ordering the things different, you get:

lim     f(g(x))-f(g(x0))*g(x)-g(x0)=df/dg*dg/dxx->x0       g(x)-g(x0)     x-x0

Now, it is easy to see that:
df/dx=df/dg*dg/dx

[edited by - danielf on June 9, 2004 8:42:13 PM]

Zipster

2,420

June 10, 2004 02:32 AM

quote:Original post by SpaceDude
That must be a pretty fancy calculator you''ve got there if it can calculate derivates for you using symbols.

Probably just a TI-89.

alvaro

21,604

June 10, 2004 10:59 AM

danielf''s "proof" is not valid. g(x0)-g(x) could be 0 in many, many points, which would make the whole argument fail.

You can find a better proof here, for instance: http://www.shu.edu/projects/reals/cont/proofs/diffalg.html

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