For (dq/dx), I understand that differentiating it will get value 'a'.

However, my concern is differentiating (dx/dq) where r is a constant.

the question wants me to differentiate dq/dx with y treated as a constant and dx/dq with r treated as a constant.

Hi,

Thank you for the guidance. However I am stuck at this part which you mentioned:

 sin(X) sin(Y) sin(-X - Y + Pi)

How come your next step eliminate the Pi and change -X and -Y to X and Y.
 f := (X, Y) -> sin(X) sin(Y) sin(X + Y)
 

Thank you.