Re: How to calculate the partial derivative?

*To*: mathgroup at smc.vnet.net*Subject*: [mg128752] Re: How to calculate the partial derivative?*From*: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>*Date*: Fri, 23 Nov 2012 03:28:14 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Dear all, I am trying to calculate the partial derivative by mathematica, I have the following commands: L1=a1+b1*x+c1*y; L2=a2+b2*x+c2*y; L3=a3+b3*x+c3*y; NN=L1*L2; DNx=D[NN,x]; I got the following result: DNex=b2 (a1+b1 x+c1 y)+b1 (a2+b2 x+c2 y) How to do to have the following result? DNex=b2*L1 + b1 * L2 Thanks, Tang Laoya Hi, Tang, Try the following. This is your definition and I denote the derivative result by expr: L1=a1+b1*x+c1*y; L2=a2+b2*x+c2*y; L3=a3+b3*x+c3*y; NN=L1*L2; expr=DNx=D[NN,x]//Simplify a2 b1+a1 b2+2 b1 b2 x+b2 c1 y+b1 c2 y What you want is to exclude x and y from the final expression. Let us denote L1 and L2 by l1 and l2, and find x and y from the first and the second equations: sol = Solve[{l2 == a2 + b2*x + c2*y, a1 + b1*x + c1*y == l1}, {x, y}][[1]] {x -> -((a2 c1 - a1 c2 + c2 l1 - c1 l2)/(b2 c1 - b1 c2)), y -> -((-a2 b1 + a1 b2 - b2 l1 + b1 l2)/(b2 c1 - b1 c2))} Now substitute it into the result: expr /. sol // Simplify b2 l1 + b1 l2 Have fun, Alexei Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L-5326 Contern, LUXEMBOURG Office phone : +352-2454-2566 Office fax: +352-2454-3566 mobile phone: +49 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu