Question

How do you find the derivative of `arcsin x + arccos x`?

Answer 1

This is single valued and equals the constant `pi/2`, if and only if its range is specified as #[alpha, alpha+pi/2], and in this case, the derivative is 0. Otherwise, it is not differentiable.

Explanation:

If u = arc sin x and v = arc cos x, u + v is many valued and is of the

form of an odd multiple of `pi/2`.

u + v is single valued and equals the constant `pi/2`, if and only if its

range is specified as #[alpha, alpha+pi/2], and in this case, the

derivative is 0. Here, `alpha` is arbitrary.

Otherwise, it is not differentiable.