`y x+1/x=7,f i n dx^3+1/(x^3)`

If x^3+y^3+3a x y=0 , f i n d dy / dx

If x^3+y^3+3a x y=0 , f i n d dy / dx

If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)),"f i n d"(dy)/(dx)

y=tan^(- 1)sqrt((1-x)/(1+x))f i n d(dy)/(dx)

y=tan^(- 1)sqrt((1-x)/(1+x))f i n d(dy)/(dx)

If y = 1 +x +(x^2)/(2!)+x^3/(3!)+....+ x^n(n!) then (dy)/(dx) is equal to

Match the following {:("List - I "," List II "),( (A) int (f^(1)(x))/(f(x)) dx = ,(1) 2 sqrt(f(x)) +c ),((B) int (f^(1)(x))/(sqrt(f(x))) dx= , (2) (2)/(3) (f(x))^(3//2) + c ),((C) int f^(1) (x) sqrt(f(x)) dx =, (3)" log | f(x)| + c"),((D) int f^(1) (x).(f(x))^(2) dx = , (4) (1)/(3) (f(x))^(3) + c ):} The correct match for list -I from List - II is

If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :