Given that the restriction of the cosine function

cos

to

I:=[0,\\\\pi ]

is strictly decreasing and that\

cos0=1,cos\\\\pi =-1

, let

J:=[-1,1]

, and let Arccos:

J->R

be the function inverse to the\ restriction of cos to

I

. Show that Arccos is differentiable on

(-1,1)

and

D

Acrccos

y=

\

(-1)/((1-y^(2))^((1)/(2)))

for

yin(-1,1)

. Show that Arccos is not differentiable at -1 and 1 .

Given that the restriction of the cosine function cos to I:=[0,] is strictly decreasing and that cos0=1,cos=1, let J:=[1,1], and let Arccos: JR be the function inverse to the restriction of cos to I. Show that Arccos is differentiable on (1,1) and D Acrccos y= (1)/(1y2)1/2 for y(1,1). Show that Arccos is not differentiable at -1 and 1