" 31.Differentiate "(tan-1sqrt(1+sin x)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x))]

cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]=

Differentiate 'tan^(^^)(-1){(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))},darr backslash0

(cot^(-1){sqrt(1+sin x)+sqrt(1-sin x)})/(sqrt(1+sin x)-sqrt(1-sin x))

Differentiate tan^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) w.r.t.x .

cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2)

the expression ((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=

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

Differentiate w.r.t x : tan^-1{(sqrt (1+sin x) + sqrt (1-sin x))/(sqrt (1+sin x) - sqrt (1-sin x))}, 0 < x < pi/2

Differentiate w.r.t x the functions cot ^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]

Differentiate tan^(-1) ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) w.r.t. x .