Mister Exam

Derivative of (x-3)e^-x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         -x
(x - 3)*E  
$$e^{- x} \left(x - 3\right)$$
(x - 3)*E^(-x)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    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 - 3)*e  
$$- \left(x - 3\right) e^{- x} + e^{- x}$$
The second derivative [src]
          -x
(-5 + x)*e  
$$\left(x - 5\right) e^{- x}$$
The third derivative [src]
         -x
(6 - x)*e  
$$\left(6 - x\right) e^{- x}$$