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Identical expressions
one -e^(2x)-2xe^(2x)
1 minus e to the power of (2x) minus 2xe to the power of (2x)
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1-e(2x)-2xe(2x)
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Similar expressions
1-e^(2x)+2xe^(2x)
1+e^(2x)-2xe^(2x)

The derivative of the function/ 1-e^(2x)-2xe^(2x)

Derivative of 1-e^(2x)-2xe^(2x)

The solution

You have entered [src]

     2*x        2*x
1 - e    - 2*x*e

$$- 2 x e^{2 x} - e^{2 x} + 1$$

d /     2*x        2*x\
--\1 - e    - 2*x*e   /
dx

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

Transform

Detail solution

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

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

The answer is:

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

The graph

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The first derivative [src]

     2*x        2*x
- 4*e    - 4*x*e

$$- 4 x e^{2 x} - 4 e^{2 x}$$

Simplify

The second derivative [src]

              2*x
-4*(3 + 2*x)*e

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

Simplify

The third derivative [src]

             2*x
-16*(2 + x)*e

$$- 16 \left(x + 2\right) e^{2 x}$$

Simplify

The graph

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Derivative of 1-e^(2x)-2xe^(2x)

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The solution