Mister Exam

Derivative of (3-x)*exp(x)

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      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  + (3 - x)*e 
$$\left(3 - x\right) e^{x} - e^{x}$$
The second derivative [src]
           x
-(-1 + x)*e 
$$- \left(x - 1\right) e^{x}$$
The third derivative [src]
    x
-x*e 
$$- x e^{x}$$