1.

`y = sin ^(-1)(2xsqrt(1 - x^(2))),-(1)/sqrt(2) lt x lt (1)/sqrt(2)`

Answer» `y sin ^(-1)(2xsqrt(1-x^(2)))`
Let `x = sin theta`
`rArr theta= sin ^(-1)x`
`rArr y = sin^(-1)(2 sin thetasqrt(1 - sin^(2) theta))`
=` sin ^(-1)(2 sin thetacos theta)`
` sin ^(-1)(sin 2theta)= 2theta = 2 sin^(-1)x`
` (dy)/(dx)= 2 (d)/(dx) sin^(-1)x = - ((2)/(sqrt(1-x^(2))))`


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