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Find (dy)/(dx)" for "y=sin^(-1) (cos x),...

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

Text Solution

Verified by Experts

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):}`
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