multiple derivatives?

*To*: mathgroup at smc.vnet.net*Subject*: [mg45340] multiple derivatives?*From*: Michael Alfaro <malfaro at ucsd.edu>*Date*: Thu, 1 Jan 2004 05:54:32 -0500 (EST)*References*: <200312271000.FAA02128@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi all, I have been struggling with the following problem and would be grateful for any advice on how to proceed. The rather ugly function below (uKT) describes a four-bar mechanism found in the jaws of some fishes and relates lower jaw opening to motion expressed at another jaw bone (uKT is a measure of mechanical advantage). (uDiagonal[input_, fixed_, angleA_] := Sqrt[input^2 + fixed^2 - 2*input*fixed*Cos[angleA*(Pi/180)]]; )* (uAngYZ[fixed_, input_, coupler_, output_, angleA_] := ArcCos[(coupler^2 + output^2 - uDiagonal[input, fixed, angleA]^2)/(2*coupler*output)]*(180/Pi); )* (uAngW[fixed_, input_, coupler_, output_, angleA_] := ArcCos[(uDiagonal[input, fixed, angleA]^2 + fixed^2 - input^2)/ (2*uDiagonal[input, fixed, angleA]*fixed)]*(180/Pi); )* (uAngX[fixed_, input_, coupler_, output_, angleA_] := ArcCos[(coupler^2 + uDiagonal[input, fixed, angleA]^2 - output^2)/ (2*coupler*uDiagonal[input, fixed, angleA])]*(180/Pi); )* (uAngY[f_, i_, c_, o_, A_] := 90 - uAngW[f, i, c, o, A] - uAngX[f, i, c, o, A]; )* (uAngZ[f_, i_, c_, o_, A_] := uAngYZ[f, i, c, o, A] - uAngY[f, i, c, o, A]); uKT[f_, i_, c_, o_, A_] := (uAngZ[f, i, c, o, A + 30] - uAngZ[f, i, c, o, A])/30 uKT[1, 0.409923448, 0.420293528, 0.558332627, 30] I am interested in how uKT changes as a of function to i, c, and o, and have been calculating partial derivatives of each of these variables for a number of fish species. Here is an example of the partial derivative of i evaluated for one species : Derivative[0, 1, 0, 0, 0][uKT][1, 0.7`, 0.9`, 0.74`, 30] However, what I would really like to know is, given a unit small amount of change that can be distributed over all three variables in any way, how much does uKT change. I initially thought that I could get at that by taking the multiple derivative of all three variables. Derivative[0, 1, 1, 1, 0][uKT][1, 0.7`, 0.9`, 0.74`, 30] However, I now have doubts that the multiple partial derivative actually tells me this. Does anyone have any insight into this problem? Thanks! Michael