" (i) "tan^(-1)((sqrt(x)(3-x))/(1-3x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=

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))

The value of (d)/(dx) [ tan^(-1){(sqrt(x) (3-x))/(1-3x)}] is -

"tan^(-1)"((sqrt(x)-x)/(1+sqrt(x^(3))))"

If f(x)=tan^(-1)((sqrt(3)x-3x)/(3sqrt(3)+x^(2)))+tan^(-1)(x/(sqrt(3))),0lexle3, then range of f(x) is