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

1 Answer
A. S. Adikesavan
May 2, 2016

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.

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