If y=sin^(-1)((2x)/(1+x^2)), then find (...

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

Text Solution

Verified by Experts

The correct Answer is:

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

`y=sin^(-1)((2x)/(1+x^(2)))`
Let `x = tan theta.` Therefore,
`y=sin^(-1)((2tan theta)/(1+tan^(2)theta))`
`=sin^(-1)(sin 2 theta)`
`=2theta`
`=2tan^(-1)x`
`therefore" "(dy)/(dx=(d)/(dx)(2 tan^(-1)x)`
`=2(d)/(dx)(tan^(-1)x)`
`(2)/(1+x^(2))`

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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))) `

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` (-2x)/( sqrt(1-x^(4))) `

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