`(dy)/(dx)` ज्ञात कीजिए : `y=sin^(-1)(2xsqrt(1-x^(2))),-(1)/(sqrt2) lt x lt (1)/(sqrt2)`

`(dy)/(dx)` ज्ञात कीजिए : `y=sin^(-1)(2xsqrt(1-x^(

1.	`(dy)/(dx)` ज्ञात कीजिए : `y=sin^(-1)(2xsqrt(1-x^(2))),-(1)/(sqrt2) lt x lt (1)/(sqrt2)`
Answer» `y=sin^(-1)(2x sqrt(1-x^(2)))" "{:("माना "x=tan theta),(rArr theta= tan^(-1)x):}` `rArr" "y=sin^(-1)(2 sin thetasqrt(1-sin^(2) theta))` `=sin^(-1)(2sin theta cos theta)` `=sin^(-1)(sin 2theta)=2 theta=2sin^(-1)x` `rArr" "(dy)/(dx)=2(d)/(dx)sin^(-1)x=(2)/(sqrt(1-x^(2)))`