What Is The Derivative Of Arccos X?

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4 Answers

Anonymous Profile
Anonymous answered
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
Anonymous Profile
Anonymous answered
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.
Anonymous Profile
Anonymous answered
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)
marlon fuentes Profile
marlon fuentes answered
D (arc because X)

D = because^-1 X

   = 1/because X

   =[because X (0)- 1(-sin X)]/ (because X)^2

   = sin X/ (because X) (because X)

   = tan X / because X

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