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Derivative of:
Derivative of 4/x^3
Derivative of x^6/6
Derivative of x^3/x
Derivative of (x-3)^4
Identical expressions
exp^(-x^ two - two)
exponent of to the power of ( minus x squared minus 2)
exponent of to the power of ( minus x to the power of two minus two)
exp(-x2-2)
exp-x2-2
exp^(-x²-2)
exp to the power of (-x to the power of 2-2)
exp^-x^2-2
Similar expressions
exp^(x^2-2)
exp^(-x^2+2)

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

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

The solution

You have entered [src]

    2    
 - x  - 2
E

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

E^(-x^2 - 2)

Detail solution

Let $u = - x^{2} - 2$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x^{2} - 2\right)$ :
1. Differentiate $- x^{2} - 2$ term by term:
  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: $- 2 x$
  2. The derivative of the constant $-2$ is zero.
  The result is: $- 2 x$
The result of the chain rule is:

$- 2 x e^{- x^{2} - 2}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         2    
      - x  - 2
-2*x*e

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

Simplify

The second derivative [src]

                     2
  /        2\  -2 - x 
2*\-1 + 2*x /*e

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

Simplify

The third derivative [src]

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

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

Simplify