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(x)*(exp(-x^2))

Derivative of (x)*(exp(-x^2))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     2
   -x 
x*e   
$$x e^{- x^{2}}$$
  /     2\
d |   -x |
--\x*e   /
dx        
$$\frac{d}{d x} x e^{- x^{2}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. Let .

    2. The derivative of is itself.

    3. Then, apply the chain rule. Multiply by :

      1. Apply the power rule: goes to

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

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