Mister Exam

Derivative of x*e^(-x)

Find the 200th derivative of f(x) = xe−x.
Find the 600th derivative of f(x) = xe−x.

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   -x
x*e  
$$x e^{- x}$$
d /   -x\
--\x*e  /
dx       
$$\frac{d}{d x} x e^{- x}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. The derivative of is itself.

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 -x      -x
e   - x*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  
$$\left(3 - x\right) e^{- x}$$
The graph
Derivative of x*e^(-x)