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

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Alexei Boulbitch

Posts: 483
Registered: 2/28/08
Re: How to calculate the partial derivative?
Posted: Nov 23, 2012 3:30 AM
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Dear all,

I am trying to calculate the partial derivative by mathematica, I have the following commands:



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

Tang Laoya

Hi, Tang,

Try the following.

This is your definition and I denote the derivative result by expr:




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,

{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.
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