Home
Class 12
MATHS
If y = x + e^(x) , then ( d^(2) x)/( ...

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))^(2)` d)`(-1)/( (1 + e^(x))^(3))`

A

`e^(x)`

B

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

C

`-(e^(x))/((1 + e^(x))^(2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

int(e^(-x))/(1+e^(x))dx=

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

The general solution of the differential equation (dy)/(dx) = e^(y) (e^(x) + e^(-x) + 2x) is a) e^(-y) = e^(x) - e^(-x) + x^(2) + C b) e^(-y) = e^(-x) - e^(x) - x^(2) + C c) e^(-y) = -e^(-x) - e^(x) - x^(2) + C d) e^(y) = e^(-x) + e^(x) + x^(2) + C

int_(-1)^(1)(e^(x^(3)) + e^(-x^(3)))(e^(x) - e^(-x)) dx is equal to

(e^x+e^(-x)) d y-(e^x-e^(-x)) d x=0

int (xe ^(x))/( (1 + x )^(2)) dx is equal to a) ( - e ^(x))/( x +1) + C b) (e ^(x))/( x +1 ) + C c) (xe ^(x))/( x +1)+ C d) (- xe ^(x))/( x +1 ) +C

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

int(2e^(5x)+e^(4x)-4e^(3x)+4e^(2x)+2e^(x))/((e^(2x)+4)(e^(2x)-1)^(2))dx= a) "tan"^(-1)(e^(x))/(2)-(1)/(e^(2x)-1)+C b) "tan"^(-1)e^(x)-(1)/(2(e^(2x)-1))+C c) "tan"^(-1)(e^(x))/(2)-(1)/(2(e^(2x)-1))+C d) 1-"tan"^(-1)((e^(x))/(2))+(1)/(2(e^(2x)-1))+C

int ((1 + x ) e ^(x))/( sin ^(2) (xe ^(x))) dx is equal to a) - cot (e ^(x)) + C b) tan (xe ^(x)) + C c) tan (e ^(x)) + C d) -cot (x e ^(x)) + C