Question

What is the derivative of `sin((pi/2) - x)`?

Answer 1

`-sinx`

Explanation:

`sin(pi/2-x) = cos x`, so

`d/dx(sin(pi/2-x) ) = d/dx(cosx) = -sinx`

If, for some reason, you don't want to simplify the expression, use

`d/dx sin(u) = cos u * (du)/dx` to get

`d/dx(sin(pi/2-x) ) = cos(pi/2-x)* d/dx(pi/2-x)`

`= - cos(pi/2-x)`.