`d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=` `1/(2(1+x)sqrt(x))` (b) `3/((1+x)sqrt(x))` `2/((1+x)sqrt(x))` (d) `3/(2(1+x)sqrt(x))`

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

(1)/(sqrt(x+3)-sqrt(x-4))

int_(1)^(2)(sqrt(x))/(sqrt(3-x)+sqrt(x))dx .

(sqrt(x)+(1)/(sqrt(x)))^(2)

IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s a. 1/2((sqrt(x^2-1))/(x^3)+tan^(-1)sqrt(x^2-1))+C b. 1/2((sqrt(x^2-1))/(x^2)+xtan^(-1)sqrt(x^2-1))+C c. 1/2((sqrt(x^2-1))/x+tan^(-1)sqrt(x^2-1))+C d. 1/2((sqrt(x^2-1))/(x^2)+tan^(-1)sqrt(x^2-1))+C

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

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

Show that int_(3)^(4)(sqrt(x))/(sqrt(7-x)+sqrt(x))dx=(1)/(2)

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4