Mister Exam

Other calculators


x^3*e^x

You entered:

x^3*e^x

What you mean?

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 
$$x^{3} e^{x}$$
d / 3  x\
--\x *e /
dx       
$$\frac{d}{d x} x^{3} e^{x}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. The derivative of is itself.

    The result is:

  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  + 9*x  + 18*x/*e 
$$\left(x^{3} + 9 x^{2} + 18 x + 6\right) e^{x}$$
The graph
Derivative of x^3*e^x