The arccosine function is the inverse of the cosine function restricted to a domain on which cosine is one-to-one (conventionally [0, pi]), defined so that it takes inputs in [-1, 1] and outputs angles in [0, pi]; its graph is obtained by reflecting the restricted cosine curve across the line y = x. Using implicit differentiation on the defining relation cos(y) = x, together with the Pythagorean identity to re-express sin(y) in terms of x, yields the derivative d/dx[arccos(x)] = -1/sqrt(1 - x^2). This belongs to calculus, within the study of inverse functions and implicit differentiation applied to trigonometric functions.
The arccosine function is the inverse of the cosine function restricted to a domain on which cosine is one-to-one (conventionally [0, pi]), defined so that it takes inputs in [-1, 1] and outputs angl…