" 3."(x+1)/((x-1)sqrt(x+2))

(1)/(sqrt(x)+sqrt(x+1))+(1)/(sqrt(x+1)+sqrt(x+2))+(1)/(sqrt(x+2)+sqrt(x+3))+...(1)/(sqrt(x+98)+sqrt(x+99))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

(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)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= (a) 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)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

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))

If y=(1)/(3)"log" (x+1)/(sqrt(x^(2)-x+1))+(1)/(sqrt(3))"tan"^(-1)(2x-1)/(sqrt(3)) , show that, (dy)/(dx)=(1)/(x^(3)+1)

If 3sqrt(3sqrt(x-(1)/(3sqrt(x))=2 , then 3sqrt(x)+((1)/(3sqrt(x))) =___________

If 3sqrt(3sqrt(x-(1)/(3sqrt(x))=2 , then 3sqrt(x)((1)/(3sqrt(x))) =___________

If x>1 and (sqrt(x+1)+sqrt(x-1))/(sqrt(x+1)-sqrt(x-1))=2 then x