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Derivative of:
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Derivative of x^(-2)
Identical expressions
e^(-6x^ two)-6x
e to the power of ( minus 6x squared ) minus 6x
e to the power of ( minus 6x to the power of two) minus 6x
e(-6x2)-6x
e-6x2-6x
e^(-6x²)-6x
e to the power of (-6x to the power of 2)-6x
e^-6x^2-6x
Similar expressions
e^(6x^2)-6x
e^(-6x^2)+6x

The derivative of the function/ e^(-6x^2)-6x

Derivative of e^(-6x^2)-6x

The solution

You have entered [src]

     2      
 -6*x       
e      - 6*x

$$- 6 x + e^{- 6 x^{2}}$$

  /     2      \
d | -6*x       |
--\e      - 6*x/
dx

$$\frac{d}{d x} \left(- 6 x + e^{- 6 x^{2}}\right)$$

Transform

Detail solution

Differentiate $- 6 x + e^{- 6 x^{2}}$ term by term:
1. Let $u = - 6 x^{2}$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 6 x^{2}\right)$ :
  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: $- 12 x$
  The result of the chain rule is:
  
  $- 12 x e^{- 6 x^{2}}$
4. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $6$
  So, the result is: $-6$
The result is: $- 12 x e^{- 6 x^{2}} - 6$

The answer is:

$- 12 x e^{- 6 x^{2}} - 6$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               2
           -6*x 
-6 - 12*x*e

$$-6 - 12 x e^{- 6 x^{2}}$$

Simplify

The second derivative [src]

                     2
   /         2\  -6*x 
12*\-1 + 12*x /*e

$$12 \cdot \left(12 x^{2} - 1\right) e^{- 6 x^{2}}$$

Simplify

The third derivative [src]

                      2
      /       2\  -6*x 
432*x*\1 - 4*x /*e

$$432 x \left(- 4 x^{2} + 1\right) e^{- 6 x^{2}}$$

Simplify

The graph

Derivative of e^(-6x^2)-6x