If `x+y=3e^2t h e d/(dx)(x^y)=0forx=` `e^2` b. `e^e` c. `e` d. `2e^2`

d/dx( e^(x+5logx))

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=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=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

Statement 1: If differentiable function f(x) satisfies the relation f(x)+f(x-2)=0AAx in R , and if ((d/(dx)f(x)))_(x=a)=b ,t h e n((d/(dx)f(x)))_(a+4000)=bdot Statement 2: f(x) is a periodic function with period 4.

inte^x^4(x+x^3+2x^5)e^x^2dxis equal to 1/2x e^x^2e^x^4+c (b) 1/2x^2e^x^4+c 1/2e^x^2e^x^4+c (d) 1/2x^2e^x^2e^x^4+c

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0 .

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

Suppose f(x)=(d)/(dx)(e^(x)+2) . Find int(f(x)+x^(2))dx