If `f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]|` then coefficient of `x` in `f(x)` is

If f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

If f(x) =x^3 +x^2 +x+1 then the coefficient of x in f(x+5) is

If f(x) =x^3 +x^2 +x+1 then the coefficient of x in f(x+5) is

If f(x) =x^4 + 3x ^2 - 6x -2 then the coefficient of x^3 in f(x +1) is

If f(x) =x^4 + 3x ^2 - 6x -2 then the coefficient of x^3 in f(x +1) is

Let f(x) = 1 - x +x^2-x^3+......+x^16+x^17 , then coefficient of x^2 in f(x-1) is?

If f(x)=(x-1)(2x-3), x in [1,3] , then

If f(x)= [[x,x^2,x^3],[1,2x,3x^2],[0,2,6x]] find f'(x)

If F(x)=|[x,x^2,x^3],[1,2x,3x^2],[0,2,6x]| , then F'(x) is