If `y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x))`,then `(dy)/(dx)`is equal to (a)`(a y)/(xsqrt(a^2-x^2))` (b) `(a y)/(sqrt(a^2-x^2))` (c)`(a y)/(xsqrt(a^2-x^2))` (d) none of these

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

If sqrt(x) + sqrt(y)=4,then (dx)/(dy)at y=1.

If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) (b) 1/2 (c) 1 (d) sqrt(2)

If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) (b) 1/2 (c) 1 (d) sqrt(2)

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e nfin d(dy)/(dx)dot

y = sqrt(xsqrt(x^(2)sqrt(x^(3)sqrt(x^(4)sqrt(x^(5).....oo))))), then (dy/dx) at x = 2 is equal to

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

Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a) 1/(2y-1) (b) x/(x+2y) (c) 1/(sqrt(1+4x) (d) y/(2x+y)