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sin^(-1)(1-x^(2))...

`sin^(-1)(1-x^(2))`

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Let `y=sin^(-1)(1-x^(2))`
`therefore (dy)/(dx)=(d)/(dx)[sin^(-1)(1-x^(2))]`
`=(1)/(sqrt(1-(1-x^(2))^(2))).(d)/(dx)(1-x^(2))`
`=(1)/(sqrt(1-(1-x^(2))^(2)))(0-2x)`
`=(-2x)/(sqrt(1-(1-x^(2))^(2)))`
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Knowledge Check

  • Range of sin^(-1)((x^(2)+1)/(x^(2)+2)) is

    A
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    B
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    C
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    A
    `(0,pi/2)`
    B
    `[0,pi/2)`
    C
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    D
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