Mister Exam

Derivative of x*exp(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   x
x*e 
$$x e^{x}$$
x*exp(x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. The derivative of is itself.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   x    x
x*e  + e 
$$x e^{x} + e^{x}$$
The second derivative [src]
         x
(2 + x)*e 
$$\left(x + 2\right) e^{x}$$
The third derivative [src]
         x
(3 + x)*e 
$$\left(x + 3\right) e^{x}$$
The graph
Derivative of x*exp(x)