Mister Exam

You entered:

y=x^2ex

What you mean?

Derivative of y=x^2ex

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2  x
x *E 
$$e^{x} x^{2}$$
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]
 2  x        x
x *e  + 2*x*e 
$$x^{2} e^{x} + 2 x e^{x}$$
The second derivative [src]
/     2      \  x
\2 + x  + 4*x/*e 
$$\left(x^{2} + 4 x + 2\right) e^{x}$$
The third derivative [src]
/     2      \  x
\6 + x  + 6*x/*e 
$$\left(x^{2} + 6 x + 6\right) e^{x}$$
The graph
Derivative of y=x^2ex