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Let f(x) = tan^(-1)(((x-2))/(x^(2)+2x+2)...

Let `f(x) = tan^(-1)(((x-2))/(x^(2)+2x+2))`,then `26 f'(1)` is

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Knowledge Check

  • If f(x)=tan^(-1) ((2x)/(1-x^(2))), x in R "then "f'(x) is given by

    A
    `f'(x)=(2)/(1+x^(2))"for all x"in R (-1,1)`
    B
    `f'(x)=(2)/(1+x^(2))"for all x"in R`
    C
    `F'(x)={{:(,(2)/(1+x^(2)),"if "|x| le 1),(,(-2)/(1+x^(2)),"if |x| gt 1):}`
    D
    `f'(x)={{:(,(2)/(1+x^(2)),"if "|x| lt 1),(,(-2)/(1+x^(2)),"if |x| gt 1):}`

  • Let f(x) = sin^(-1)((2x)/(1+x^(2))) Statement I f'(2) = - 2/5 and Statement II sin^(-1)((2x)/(1 +x^(2))) = pi - 2 tan^(-1) x, AA x gt 1

    A
    Statement I is True, Statement II is True, Statement II is a correct explanation for statement I
    B
    Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I
    C
    Statement I is True, Statement II is False
    D
    Statement I is False, Statement II is True.

  • If f(x) = tan^(-1) ((2cot^(2)x)/(1 + cos^(2)x)) then d/(dx) (f(f(x))) at x = pi/2 is

    A
    0
    B
    1
    C
    `-1`
    D
    `1/2`

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