If a,b,c are sides of a triangle and A,B,C are the opposite angles, calculate бA/бa, бA/бb, бA/бc by implicit differentiation of the Law of Cosines.

Any help would be appreciated!

- October 9th 2008, 09:18 PMleungstaCalculating partial derivatives by implicit differentiation of the Law of Cosines
If a,b,c are sides of a triangle and A,B,C are the opposite angles, calculate бA/бa, бA/бb, бA/бc by implicit differentiation of the Law of Cosines.

Any help would be appreciated! - October 10th 2008, 07:29 AMGreengoblin
the cosine rule is

1.)

2.)

First the tricky bit:

let

then

3.)

similar to number 2, we use the product rule again on but this time with respect to c...this time yielding:

P.S. Someone more experienced might want to check this for you. I think it's ok though.