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" If "y=sqrt((1-x)/(1+x))," then "(1=x^(...

`" If "y=sqrt((1-x)/(1+x))," then "(1=x^(2))(dy)/(dx)` is equal to

A

`y^(2)`

B

`1//y`

C

`-y`

D

`-y//x`

Text Solution

Verified by Experts

`"We have "y=sqrt((1-x)/(1+x)`
Differentiating w.r.t. x, we get
`(dy)/(dx)=(1)/(2)((1-x)/(1+x))^(1//2-1)(d)/(dx)((1-x)/(1+x))`
`=(1)/(2)sqrt((1+x)/(1-x))cdot((1+x)(-1)-(1-x)(1))/((1+x)^(2))`
`=-sqrt((1+x)/(1-x))(1)/((1+x)^(2))`
`"or "(1-x)^(2)(dy)/(dx)=-sqrt((1+x)/(1-x))(1)/((1+x)^(2))(1-x)^(2)`
`"or "(1-x)^(2)(dy)/(dx)=-sqrt((1-x)/(1+x))`
`"or "(1-x^(2))(dy)/(dx)=-y`
`"or "(1-x^(2))(dy)/(dx)+y=0`
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Knowledge Check

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

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    C
    `sqrt(x) - (1)/(sqrt(x))`
    D
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  • If y = tan^(-1)((x)/(sqrt(1 -x^2))) , then (dy)/(dx) is equal to

    A
    `-1/(sqrt(1 - x^2))`
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