If `f(x)=2sin^(-1)sqrt(1-x)+sin^(-1)(2sqrt(x(1-x)))` , where `x in (0,1/2),t h e nf^(prime)(x)` is (a)`2/(sqrt(x(1-x)))` (b) zero (c)`-2/(sqrt(x(1-x)))` (d) `pi`

If f(x) = 2 sin^(-1)sqrt(1-x) +sin^(-1)(2-sqrt(x(1-x)) where x in (0,(1)/2) , then f'(x) is

If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in (0, 1/2) , then f'(x) has the value equal to (i) 2/(xsqrt(1-x)) (ii) 0 (iii) -2/(xsqrt(1-x)) (iv) pi

If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in (0, 1/2) , then f'(x) has the value equal to (i) 2/(xsqrt(1-x)) (ii) 0 (iii) -2/(xsqrt(1-x)) (iv) pi

int(e^x[1+sqrt(1-x^2)sin^-1x])/sqrt(1-x^2)dx

int(e^x[1+sqrt(1-x^2)sin^-1x])/sqrt(1-x^2)dx

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

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

If f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x) is equal to