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=sinx+e^x ,t h e n(d^2x)/(dy^2)= (a) (-sinx+e^x)^(-1) (b) (sinx-e^x)/((cosx+e^x)^2) (c) (sinx-e^x)/((cosx+e^x)^3) (d) (sinx+e^x)/((cosx+e^x)^3)

If y=a e^(m x)+b e^(-m x), then (d^(2y))/(dx^2)-m^2y is equal to m^2(a e^(m x)-b e^(-m x)) 1 (c) 0 (d) none of these

(dy)/(dx) = e^(2x-y) + x^(3) e^(-y)

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

(1 + e^(x/y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0

int(e^(3x)-e^(-3x))/(e^(3x)+e^(-3x))dx

int(e^(x)+1)/(e^(x))dx :

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a) (e^(sqrt(x)))/(2sqrt(x)) (b) (e^(sqrt(x))-e^(-sqrt(x)))/(2x) 1/(2sqrt(x))sqrt(y^2-4) (d) 1/(2sqrt(x))sqrt(y^2+4)

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5