Mister Exam

Other calculators


x^3/e^x

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]
 3
x 
--
 x
E 
$$\frac{x^{3}}{e^{x}}$$
x^3/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]
   3  -x      2  -x
- x *e   + 3*x *e  
$$- x^{3} e^{- x} + 3 x^{2} e^{- x}$$
The second derivative [src]
  /     2      \  -x
x*\6 + x  - 6*x/*e  
$$x \left(x^{2} - 6 x + 6\right) e^{- x}$$
The third derivative [src]
/     3             2\  -x
\6 - x  - 18*x + 9*x /*e  
$$\left(- x^{3} + 9 x^{2} - 18 x + 6\right) e^{- x}$$
The graph
Derivative of x^3/e^x