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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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