Find `(dy)/(dx)` if `y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x)-1)/(sqrt(x)+1))`

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

Evaluate int(1)/(sqrt(x+1)+sqrt(x))dx .

int(2sin^(-1)x)/(sqrt(1-x^(2)))dx

Find (dy)/(dx) for the function: y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(x)

Find (dy)/(dx) in the following : y= sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2)) .

y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt(2)) lt x lt (1)/(sqrt(2)) .

Evaluate intsqrt((3-x)/(3+x))*sin^(- 1)(1/(sqrt(6))sqrt(3-x)) dx

Integrate the functions (sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these