Question

dy/dx cos x = -sine x
why the answer in calculator isn't the same when i am using degree mode

but it is same in radian mode, does that equation only true when x is in radian?

Answer 1

It is true in radians, yes.

If you use degrees, i.e., x is in degrees, then the function is cos(pi.x/180). Hence, in degrees,
(d/dx) cos(pi.x/180) = -pi/180 . sin(pi.x/180)

Answer 2

ok ^^ i get it