" (i) "(1+x)^(x)

If y=(1+1/x)^x , then (dy)/(dx)= (a) (1+1/x)^x{log(1+1/x)-1/(x+1)} (b) (1+1/x)^xlog(1+1/x) (c) (x+1/x)^x{log(x+1)-x/(x+1)} (d) (x+1/x)^x{log(1+1/x)+1/(x+1)}

If f(x)= ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ​ 1 2x 3x(x−1) ​ x x(x−1) x(x−1)(x−2) ​ x+1 (x+1)x (x+1)x(x−1) ​ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ​ Then f(100) is equal to

If f(x)=|(1, x, x+1), (2x, x(x-1), (x+1)x), (3x(x-1), x(x-1)(x-2), (x+1)x(x-1))| then f(5000) is equal to 0 b. 1 c. 500 d. -500

If f(x)=|\(1,x,x+1),(2x,x(x-1),(x+1)x,3x(x-1),x(x-1)(x-2),(x+1)x(x-1))| then f(100) is equal to (A) 0 (B) 1 (C) 100 (D) -100

If f(x)=|\(1,x,x+1),(2x,x(x-1),(x+1)x,3x(x-1),x(x-1)(x-2),(x+1)x(x-1))| then f(100) is equal to (A) 0 (B) 1 (C) 100 (D) -100

If f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1))|, then f(100) is equal to - (i) 0 (ii) 1 (iii) 100 (iv) -100

If f(x) =|(1, x, x+1),(2x, x(x-1), x(x+1)), (3x(x-1), 2(x-1)(x-2), x(x+1)(x-1))| then what is f(-1) +f(0) +f(1) equal to ?

If y=(1+(1)/(x))^(x), then (dy)/(dx)=(1+(1)/(x))^(x){log(1+(1)/(x))-(1)/(x+1)}(b)(1+(1)/(x))^(x)log(1+(1)/(x))(c)(x+(1)/(x))^(x){log(x+1)-(x)/(x+1)}(d)(x+(1)/(x))^(x){log(1+(1)/(x))+(1)/(x+1)}

If f(x) =|(1,x,(x+1)),(2x,x(x-1),(x+1)x),(3x(x-1), x(x-1)(x-2),x(x-1)(x+1))| then f(50)+f(51)..f(99) is equal to