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Topic: How to calculate the partial derivative?
Replies: 4   Last Post: Nov 23, 2012 3:35 AM

 Messages: [ Previous | Next ]
 Alexei Boulbitch Posts: 483 Registered: 2/28/08
Re: How to calculate the partial derivative?
Posted: Nov 23, 2012 3:30 AM

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,
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Office phone : +352-2454-2566
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e-mail: alexei.boulbitch@iee.lu

Date Subject Author
11/22/12 Bob Hanlon
11/23/12 Alexei Boulbitch
11/23/12 Bob Hanlon
11/23/12 Bob Hanlon