InterviewSolution
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InterviewSolution
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The derivative of `sin^(-1)(3x-4x^(3))` with respect to `sin^(-1)x,` isA. `3," for "|x|lt1`B. `3," for "|x|lt(1)/(2)" and "-3" for "(1)/(2)lt|x|lt1`C. `-3," for "|x|lt12`D. `-3," for "|x|le(1)/(2)" and "3" for "(1)/(2)lt|x|lt1` |
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Answer» Correct Answer - B We have, `y=sin^(-1)(3x-4x^(3))={{:(3sin^(-1)x" ,"," if "|x|le(1)/(2)),(pi-3sin^(-1)x" ,"," if "(1)/(2)ltxle1),(-pi-3sin^(-1)x","," if "-1lexlt-(1)/(2)):}` Let`z=sin^(-1)x.` Then, `y={{:(3z" ,"," if "|x|le(1)/(2)),(pi-3z" ,"," if "(1)/(2)ltxle1),(-pi-3z","," if "-1lexlt-(1)/(2)):}` `implies" "(dy)/(dz)={{:(3" ,"," if "|x|lt(1)/(2)),(-3","," if "(1)/(2)lt|x|lt1):}` |
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