Find `(dy)/(dx)` for `y=sin^(-1)(cosx),` where `x in (0,2pi)dot`

Explanation

We have,
`sin^(-1)(cos x)=(pi)/(2)-cos^(-1)(cos x)`
`={:{((pi)/(2)-"x,"," "if 0ltxltpi),((pi)/(2)-(2pi-x)","," "if piltxlt2pi):}`
`={:{((pi)/(2)-"x,"," "if 0ltxltpi),(x-(3pi)/(2)-(2pi-x)","," "if piltxlt2pi):}`
`therefore" "(d)/(dx){sin^(-1)(cos x)}={:{(-1","," "if 0ltxltpi),(1","," "if piltxlt2pi):}`