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!