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

Find dy/dx in the following : y=sin^(-1)(2xsqrt(1-x^(2))),-1/sqrt2ltxlt1/sqrt2 .

Show that (i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

The derivative of sin^(-1)(2xsqrt(1-x^2)) w.r.t. sin^(-1)x,(1)/(sqrt2) lt x lt 1 is :

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

y = sin ^(-1)((1 - x^(2))/(1+ x^(2))) 0 lt x lt 1

Differentiate sin^(-1)(2xsqrt(1-x^2)), -1/(sqrt(2))

The derivative of sin^(-1) (2x sqrt(1-x^(2)))" w.r.t. "sin^(-1)x, (1)/(sqrt(2)) lt x lt 1 , is:

Prove that sin^(-1) (2xsqrt(1-x^2))=2cos^(-1)x,1/sqrt2 le x le 1

y = sec^(-1)((1)/(2x^(2) -1 )), 0 lt x lt (1)/(sqrt(2))

Express in terms of : sin^(-1)(2xsqrt(1-x^(2))) to sin^(-1)x for 1gexgt1/(sqrt(2))