InterviewSolution
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InterviewSolution
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Differentiate`sin^(-1)((2x)/(1+x^2))`with respectto `tan^(-1)((2x)/(1-x^2)),`if `-1A. 1 for all xB. `1" for "|x|gt1" and"-1" for "|x|lt1`C. `1" for "|x|lt1" and"-1" for "|x|gt1`D. `1" for "|x|le1" and"-1" for "|x|gt1` |
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Answer» Correct Answer - C Let `y=tan^(-1)((2x)/(1-x^(2)))" and "x=sin^(-1)((2x)/(1+x^(2))).` Then, `y={{:(2tan^(-1)x" ,","if"-1ltxlt1),(2tan^(-1)x-pi","," if "xgt1),(2tan^(-1)x+pi","," if "xlt-1):}` and, `z={{:(2tan^(-1)x" ,","if"-1lexle1),(pi-2tan^(-1)x" ,"," if "xgt1),(-pi-2tan^(-1)x","," if "xlt-1):}` `:." "(dy)/(dz)={{:(1" ,"," if"-1ltxlt1),(-1","," if "|x|gt1):}` |
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