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Derivative of:
Derivative of 6^x
Derivative of 2/sqrt(x)
Derivative of (x^2-1)/(x^2+1)
Derivative of x*e^(1/x)
Integral of d{x}:
exp(-x^2)
Graphing y =:
exp(-x^2)
Limit of the function:
exp(-x^2)
Identical expressions
exp(-x^ two)
exponent of ( minus x squared )
exponent of ( minus x to the power of two)
exp(-x2)
exp-x2
exp(-x²)
exp(-x to the power of 2)
exp-x^2
Similar expressions
x*exp(-x^2)
exp(x^2)

The derivative of the function/ exp(-x^2)

Derivative of exp(-x^2)

The solution

You have entered [src]

   2
 -x 
e

$$e^{- x^{2}}$$

  /   2\
d | -x |
--\e   /
dx

$$\frac{d}{d x} e^{- x^{2}}$$

Transform

Detail solution

Let $u = - x^{2}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x^{2}\right)$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $- 2 x$
The result of the chain rule is:

$- 2 x e^{- x^{2}}$

The answer is:

$- 2 x e^{- x^{2}}$

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

$$2 \cdot \left(2 x^{2} - 1\right) e^{- x^{2}}$$

Simplify

The third derivative [src]

                  2
    /       2\  -x 
4*x*\3 - 2*x /*e

$$4 x \left(- 2 x^{2} + 3\right) e^{- x^{2}}$$

Simplify

The graph

Derivative of exp(-x^2)