Derivative of (x - sin (pi x/2))?

Answer 1

f (x) = x - sin (π x / 2)
f `(x) = 1 - (π / 2) cos (π x / 2)

Answer 2

d/dx(x) - d/dx(sin[pi*x/2])
= 1 - (pi/2) * cos [pi*x/2]

For the second term, I always remember it as "derivative of the inner term, times the derivative of the outer term".

In this case, the inner term is pi*x/2 and its derivative is pi/2; the outer term is sin(..), and its derivative is cos(..), so you end up with (pi/2) * cos(..) which is (pi/2) * cos [pi*x/2]