Find `(dy)/(dx)" for "y=sin^(-1) (cos x), x in (0, pi)cup (pi, 2pi).`

1.	Find `(dy)/(dx)" for "y=sin^(-1) (cos x), x in (0, pi)cup (pi, 2pi).`
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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