`d/(dx)[sin^2(cot^-1(sqrt((1+x)/(1-x))))]=?`.

(d)/(dx)[sin(2tan^(-1)sqrt((1+x)/(1-x)))]=

d//dx[sin^(2)cot^(-1)""(1)/(sqrt((1+x)/(1-x)))] , is equal to -

(d)/(dx)[sin^(-1)((sqrt(1+x)+sqrt(1-x))/(2))]=

(d)/(dx)[sin^(-1)sqrt(((1-x))/(2)]=

(d)/(dx)[sin^(-1)((2^(x+1))/(1+4^(x)))]

Differentiate w.r.t. as indicated : tan^(-1)(x/(1+sqrt(1-x^(2))))" w.r.t. "sin(2cot^(-1)sqrt((1+x)/(1-x)))

(d)/(dx)[sin^(-1)x+sin^(-1)sqrt(1-x^(2))]=

d/(dx)[sin {2 cos^(-1) (sin x)}] =

(d)/(dx)[sin^(-1)(x^(2)-(1)/(2))]" at "x=0