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MathGroup Archive 2006

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RE: A problem in calculus

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72481] RE: [mg72469] A problem in calculus
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sun, 31 Dec 2006 05:35:07 -0500 (EST)

j would have to be a positive integer.

x[z_] := a4*z^4 + a3*z^3 + a2*z^2 + a1*z + 1

For the 3rd derivative, say, use

D[Sqrt[x[z]], {z, 3}]

(3*(a1 + 2*a2*z + 3*a3*z^2 + 4*a4*z^3)^3)/
   (8*(1 + a1*z + a2*z^2 + a3*z^3 + a4*z^4)^(5/2)) - 
  (3*(2*a2 + 6*a3*z + 12*a4*z^2)*(a1 + 2*a2*z + 
     3*a3*z^2 + 4*a4*z^3))/
   (4*(1 + a1*z + a2*z^2 + a3*z^3 + a4*z^4)^(3/2)) + 
  (6*a3 + 24*a4*z)/(2*Sqrt[1 + a1*z + a2*z^2 + 
      a3*z^3 + a4*z^4])

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 



From: kaipku at gmail.com [mailto:kaipku at gmail.com]

Hi

I have a problem to solve.


Let x(z)= a4*z^4+a3*z^3+a2*z^2+a1*z+1 be a polynomial in z.
I want the formula of the j'th derivative in z of (x(z))^(1/2). I think

this kind of problems should have been solved. But I do not
know where to find the formula. Could someone please find it for
me? Thank you very much!



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