If `y = (1 + sinx) (1 + sin^2x) (1 + sin^4x) (1 + sin^8x)(1 + sin ^16x)`, then the value of `dy / dx` at `x =0` is

If y= tan ^(-1) sqrt (( 1 - sin x)/( 1 + sin x)) , then the vluae of (dy)/(dx) at x = pi /2 is

If y=tan^(-1)sqrt((1-sin x)/(1+sin x)), then the value of (dy)/(dx) at x=(pi)/(6) is.

If sin y = x sin (y - a) and (dy)/(dx) = A/(1 + x^2 - 2x cos a) then the value of A is

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :