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

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

Discussion

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