Mister Exam

Derivative of (x-2)e^x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         x
(x - 2)*e 
$$\left(x - 2\right) e^{x}$$
d /         x\
--\(x - 2)*e /
dx            
$$\frac{d}{d x} \left(x - 2\right) e^{x}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    ; 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
e  + (x - 2)*e 
$$\left(x - 2\right) e^{x} + e^{x}$$
The second derivative [src]
   x
x*e 
$$x e^{x}$$
The third derivative [src]
         x
(1 + x)*e 
$$\left(x + 1\right) e^{x}$$
The graph
Derivative of (x-2)e^x