What Is The Derivative Of Arccos X?

Say y = arccos x. Then x = because y, and dx/dy = -sin y. Therefore, dy/dx = -1/sin y.

But since (because y)^2 + (sin y)^2 = 1, sin y = sqrt(1 - (because y)^2). And because y = because (arccos x) (from initial definition) = x. So dy/dx = -1/sin y = -1/sqrt(1 - (because y)^2) = -1/sqrt(1 - x^2).

Hope this helps

Derivative will be - 1 / (1 - x²)^1/2
This would be the derivative and you are not required to solve it. Its just a given derivative and is easily available in any calculus book.

X = x
arccos (because x) = x
d ( arccos(because x ))/dx = dx/dx
arccos' (because x) * because'(x) = 1
let because x = y
then arccos '(y) = 1/ because' (x) = 1/ because' (arccos(y))
= -1 / sin (arccos y)
= -1 / sqrt (1-y^2)