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If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=...

If `y=f((2x-1)/(x^2+1))` and `f^(prime)(x)=sinx^2` , find `(dy)/(dx)` .

A

`sin ((2x+1)/(x^2+1))^(2) [(2+2x-2x^(2))/(x^(2)+1)]`

B

`sin ((2x-1)/(x^(2)-1))^(2) [(2+2x-2x^(2))/(x^(2)+1)]`

C

`sin ((2x-1)/(x^(2)+1))^(2) [(2+2x-2x^(2))/(x^(2)+1)]`

D

`sin ((2x+1)/(x^(2)-1))^(2) [(2+2x-2x^(2))/(x^(2)+1)]`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If y=f((2x-1)/(x^(2)+1)) and f^'(x)=sinx^(2) , then (dy)/(dx) is equal to

    A
    `sin((2x-1)/(x^(2)+1)^(2).((2+2x+2x^(2))/((x^(2)+1)^(2))))`
    B
    `sin((2x-1)/(x^(2)+1)^(2).((2+2x-2x^(2))/((x^(2)+1)^(2))))`
    C
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    D
    `sin(x^(2)).((2+2x-2x^(2))/((x^(2)+1)^(2)))`

  • If Y=f ((2x -1)/(x^2 +1)) and f'(x) = sin x^2 , then (dy)/(dx) at x=0 equals

    A
    `1/2 sin 1 `
    B
    ` sin 1`
    C
    `2 sin 1`
    D
    None of these

  • If y=f((2x+3)/(3-2x)) and f(x)=sin(logx) , then (dy)/(dx)=

    A
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    B
    `12/(4x^2-9)cos{log""(2x+3)/(3-2x))}`
    C
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    D
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