" 7.",(i)sin^(-1)(2x sqrt(1-x^(2)))

Differentiate each of the following functions with respect to x:( i) sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

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

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

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

Differentiate each of the following functions with respect to x : (i) sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1/(sqrt(2)) (ii) cos^(-1)(2x(sqrt(1-x^2)),-1/sqrt(2)ltxlt1/sqrt2

Prove that : sin^(-1) (2x sqrt(1-x^(2)))= 2 sin^(-1) x, - 1/(sqrt(2)) le x le 1/(sqrt(2))