If `y=x+e^x,` then `(d^2x)/(dy^2)` is (a) `e^x` (b) `- e^x/((1+e^x)^3)` (c) `-e^x/((1+e^x)^3)` (d) `(-1)/((1+e^x)^3)`

If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e^x/((1+e^x)^2) (d) (-1)/((1+e^x)^3)

If y=x+e^(x), then (d^(2)x)/(dy^(2)) is (a) e^(x)(b)-(e^(x))/((1+e^(x))^(3))(c)-(e^(x))/((1+e^(x))^(3))(d)(-1)/((1+e^(x))^(3))

If y=sin x+e^(x), then (d^(2)x)/(dy^(2))= (a) (-sin x+e^(x))^(-1)(b)(sin x-e^(x))/((cos x+e^(x))^(2))(c)(sin x-e^(x))/((cos x+e^(x))^(3))(d)(sin x+e^(x))/((cos x+e^(x))^(3))

int(1)/(1+e^(x))dx= (a) log(1+e^(x)) (b) log((1+e^(x))/(e^(x))) (c) log(1+e^(-x)) (d) -log(e^(-x)+1)

int2/((e^x+e^(-x))^2)\ dx (a) ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x))+C (c) (-1)/((e^x+1)^2)+C (d) 1/(e^x-e^(-x))+C

int x^2 . e^(x^3) dx = (a) e^(x^3) + C (b) e^(x^2) + C (c) 1/3 e^(x^3) + C (d) 1/3 e^(x^2) + C

(dy)/(dx) =y ((e^(3x)-e^(-3x))/(e^(3x) +e^(-3x)))

(d)/(dx){sin^(-1)(e^(x))} is equal to (a) e^(x)sin^(-1)(e^(x)) (b) (e^(x))/(sqrt(1-e^(2x))) (c) (e^(x))/(1-e^(x)) (d) e^(x)cos^(-1)x]]

int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C (d) x e^(-x)+C

If x=e^(y+e^(y+e^y^(------ ∞))) , x>0 , then (dy)/(dx) is equal to (A) (x)/(1+x) (B) (1)/(x) (C) (1-x)/(x) (D) (1+x)/(x)