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!
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!
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.