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If y=sin ^(-1) ((2^(x+1))/( 1+4^(x))),t...

If ` y=sin ^(-1) ((2^(x+1))/( 1+4^(x))),then (dy)/(dx) =`

A

`(2^(x))/(1+4^(x))log2`

B

`(4^(x-1))/(1+4^(x))log2`

C

`(2^(x))/(1+2^(x))log2`

D

`(2^(x+1))/(1+4^(x))log2`

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Knowledge Check

  • If y =sin ^(-1) sqrt((1+x^(2))/( 2) ),then (dy)/(dx) =

    A
    ` (-x)/( sqrt(1-x^(4))) `
    B
    ` (x)/( sqrt(1-x^(4))) `
    C
    ` (-2x)/( sqrt(1-x^(4))) `
    D
    ` (2x)/( sqrt(1-x^(4))) `

  • If y=sin ^(-1)((x)/( sqrt(x^(2) +a^(2)))) ,then (dy)/(dx)=

    A
    ` (-a^(2))/( a^(2) +x^(2))`
    B
    ` (a^(2))/( a^(2) +x^(2))`
    C
    ` (-a)/( a^(2) +x^(2))`
    D
    ` (a)/( a^(2) +x^(2))`

  • If y=sin^(-1)((4x)/(1+4x^(2))) , then what is (dy)/(dx) equal to?

    A
    `(1)/(1+4x^(2))`
    B
    `-(1)/(1+4x^(2))`
    C
    `(4)/(1+4x^(2))`
    D
    `(4x)/(1+4x^(2))`

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