" 1.(a) "sin^(-1){2x sqrt(1-x^(2))};-(1)/(sqrt(2))

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

Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) with respect to sin^(-1)(2x sqrt(1-x^(2))), if -(1)/(sqrt(2))

Find (dy)/(dx) in the following: y=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

sin^(-1)(2x sqrt(1-x^(2))),x in[(1)/(sqrt(2)),1] is equal to

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