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e^(-x²)
The derivative of the function/ e^(-x²)

Derivative of e^(-x²)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2
 -x 
E
$$e^{- x^{2}}$$ 
E^(-x^2)
Detail solution

  1. Let .

  2. The derivative of is itself.

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

    1. 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 of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        2
      -x 
-2*x*e
$$- 2 x e^{- x^{2}}$$
Simplify
The second derivative [src] 
                 2
  /        2\  -x 
2*\-1 + 2*x /*e
$$2 \left(2 x^{2} - 1\right) e^{- x^{2}}$$
Simplify
The third derivative [src] 
                  2
    /       2\  -x 
4*x*\3 - 2*x /*e
$$4 x \left(3 - 2 x^{2}\right) e^{- x^{2}}$$
Simplify
The graph
Derivative of e^(-x²)
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