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=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))

(1)/(e^(3x)+e^(-3x))

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)

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)))

(xe^x)/(1+x)^2dx= (A) e^x/(1+x) (B) e^x/(1+x)^2 (C) e^xlog(1+x) (D) none of these

(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]]

If y=x^(2)e^(x),"show that "(d^(2)y)/(dx^(2))-(dy)/(dx)-2(x+1)e^(x)=0

int (e ^ (3x) + e ^ (x)) / (e ^ (4x) -e ^ (2x) +1) dx

Find (dy)/(dx) if y=e^(x)*e^(x^(2))*e^(x^(3))*e^(x^(4))