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Derivative of:
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Identical expressions
- one /2e^(2x)+c
minus 1 divide by 2e to the power of (2x) plus c
minus one divide by 2e to the power of (2x) plus c
-1/2e(2x)+c
-1/2e2x+c
-1/2e^2x+c
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Similar expressions
1/2e^(2x)+c
-1/2e^(2x)-c

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

Derivative of -1/2e^(2x)+c

The solution

You have entered [src]

   2*x    
  E       
- ---- + c
   2

c - \frac{e^{2 x}}{2}

Transform

Detail solution

Differentiate $c - \frac{e^{2 x}}{2}$ term by term:
1. 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: $- e^{2 x}$
2. The derivative of the constant $c$ is zero.
The result is: $- e^{2 x}$

The answer is:

- e^{2 x}

The first derivative [src]

  2*x
-e

- e^{2 x}

Simplify

The second derivative [src]

    2*x
-2*e

- 2 e^{2 x}

Simplify

The third derivative [src]

    2*x
-4*e

- 4 e^{2 x}

Simplify