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Expresiones con funciones
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Derivada de la función/ x*exp(-cos(x)(ln(tg(x)))-ln(tg(x/2))x)

Derivada de x*exp(-cos(x)(ln(tg(x)))-ln(tg(x/2))x)

Solución

Ha introducido [src]

                            /   /x\\  
   -cos(x)*log(tan(x)) - log|tan|-||*x
                            \   \2//  
x*e

$$x e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)}$$

x*exp((-cos(x))*log(tan(x)) - log(tan(x/2))*x)

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
$g{\left(x \right)} = e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. Sustituimos $u = - x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)$ .
2. Derivado $e^{u}$ es.
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)\right)$ :
  1. diferenciamos $- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)$ miembro por miembro:
    1. Se aplica la regla de la derivada de una multiplicación:
      
      $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
      
      $f{\left(x \right)} = - \cos{\left(x \right)}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
      1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        La derivada del coseno es igual a menos el seno:
        
        $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
        
        Entonces, como resultado: $\sin{\left(x \right)}$
      $g{\left(x \right)} = \log{\left(\tan{\left(x \right)} \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
      1. Sustituimos $u = \tan{\left(x \right)}$ .
      2. Derivado $\log{\left(u \right)}$ es $\frac{1}{u}$ .
      3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \tan{\left(x \right)}$ :
        
        Reescribimos las funciones para diferenciar:
        
        $\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
        
        Se aplica la regla de la derivada parcial:
        
        $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
        
        $f{\left(x \right)} = \sin{\left(x \right)}$ y $g{\left(x \right)} = \cos{\left(x \right)}$ .
        
        Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
        
        La derivada del seno es igual al coseno:
        
        $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
        
        Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
        
        La derivada del coseno es igual a menos el seno:
        
        $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
        
        Ahora aplicamos la regla de la derivada de una divesión:
        
        $\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
        
        Como resultado de la secuencia de reglas:
        
        $\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}}$
      Como resultado de: $- \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} \tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}$
    2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
      1. Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        $g{\left(x \right)} = \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        Sustituimos $u = \tan{\left(\frac{x}{2} \right)}$ .
        
        Derivado $\log{\left(u \right)}$ es $\frac{1}{u}$ .
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \tan{\left(\frac{x}{2} \right)}$ :
        
        Sustituimos $u = \frac{x}{2}$ .
        
        $\frac{d}{d u} \tan{\left(u \right)} = \frac{1}{\cos^{2}{\left(u \right)}}$
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{x}{2}$ :
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $\frac{1}{2}$
        
        Como resultado de la secuencia de reglas:
        
        $\frac{1}{2 \cos^{2}{\left(\frac{x}{2} \right)}}$
        
        Como resultado de la secuencia de reglas:
        
        $\frac{\frac{\sin^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{x}{2} \right)}}{2}}{\cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}}$
        
        Como resultado de: $\frac{x \left(\frac{\sin^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{x}{2} \right)}}{2}\right)}{\cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}} + \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}$
      Entonces, como resultado: $- \frac{x \left(\frac{\sin^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{x}{2} \right)}}{2}\right)}{\cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}} - \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}$
    Como resultado de: $- \frac{x \left(\frac{\sin^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{x}{2} \right)}}{2}\right)}{\cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}} - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} \tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}$
  Como resultado de la secuencia de reglas:
  
  $\left(- \frac{x \left(\frac{\sin^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{x}{2} \right)}}{2}\right)}{\cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}} - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} \tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)}$
Como resultado de: $x \left(- \frac{x \left(\frac{\sin^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{\cos^{2}{\left(\frac{x}{2} \right)}}{2}\right)}{\cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}} - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} \tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)} + e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)}$
Simplificamos:

$\frac{\left(- x^{2} - x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \sin{\left(x \right)} - \frac{x \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}}{2} + \frac{x \log{\left(\tan{\left(x \right)} \right)}}{2} - x + \sin{\left(x \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}}}{\left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}$

Respuesta:

$\frac{\left(- x^{2} - x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \sin{\left(x \right)} - \frac{x \log{\left(\tan{\left(x \right)} \right)} \cos{\left(2 x \right)}}{2} + \frac{x \log{\left(\tan{\left(x \right)} \right)}}{2} - x + \sin{\left(x \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}}}{\left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

  /                                       /       2/x\\                       \                                                                            
  |                                       |    tan |-||                       |                                                                            
  |                                       |1       \2/|                       |                           /   /x\\                               /   /x\\  
  |                                     x*|- + -------|   /       2   \       |  -cos(x)*log(tan(x)) - log|tan|-||*x    -cos(x)*log(tan(x)) - log|tan|-||*x
  |     /   /x\\                          \2      2   /   \1 + tan (x)/*cos(x)|                           \   \2//                               \   \2//  
x*|- log|tan|-|| + log(tan(x))*sin(x) - --------------- - --------------------|*e                                    + e                                   
  |     \   \2//                                /x\              tan(x)       |                                                                            
  |                                          tan|-|                           |                                                                            
  \                                             \2/                           /

$$x \left(- \frac{x \left(\frac{\tan^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{1}{2}\right)}{\tan{\left(\frac{x}{2} \right)}} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)} + e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + \log{\left(\tan{\left(x \right)} \right)} \left(- \cos{\left(x \right)}\right)}$$

Simplificar

Segunda derivada [src]

/                                           /                                                                                 2                                                                                                        2                                                   \                                           \                                      
|                                           |/                                         /       2/x\\                         \                               /       2/x\\                                                /       2/x\\                   2                                |                                           |                                      
|                                           ||                                       x*|1 + tan |-||     /       2   \       |                             4*|1 + tan |-||                                              x*|1 + tan |-||      /       2   \             /       2   \       |                                           |                                      
|                                           ||     /   /x\\                            \        \2//   2*\1 + tan (x)/*cos(x)|      /       2   \            \        \2//       /       2/x\\                            \        \2//    4*\1 + tan (x)/ *cos(x)   8*\1 + tan (x)/*sin(x)|                                           |                                      
|                                         x*||2*log|tan|-|| - 2*log(tan(x))*sin(x) + --------------- + ----------------------|  - 8*\1 + tan (x)/*cos(x) - --------------- - 2*x*|1 + tan |-|| + 4*cos(x)*log(tan(x)) + ---------------- + ----------------------- + ----------------------|                                           |                                      
|                                           ||     \   \2//                                  /x\               tan(x)        |                                     /x\           \        \2//                                 2/x\                   2                      tan(x)        |     /       2/x\\                         |         /   /x\\                     
|                                           ||                                            tan|-|                             |                                  tan|-|                                                      tan |-|                tan (x)                                 |   x*|1 + tan |-||     /       2   \       |  - x*log|tan|-|| - cos(x)*log(tan(x))
|       /   /x\\                            \\                                               \2/                             /                                     \2/                                                          \2/                                                        /     \        \2//   2*\1 + tan (x)/*cos(x)|         \   \2//                     
|- 2*log|tan|-|| + 2*log(tan(x))*sin(x) + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------- - ----------------------|*e                                    
|       \   \2//                                                                                                                                                  4                                                                                                                                    /x\               tan(x)        |                                      
|                                                                                                                                                                                                                                                                                                   tan|-|                             |                                      
\                                                                                                                                                                                                                                                                                                      \2/                             /

$$\left(- \frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{x \left(\frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\tan^{2}{\left(\frac{x}{2} \right)}} - 2 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) - \frac{4 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(x \right)}} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} - 8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} + \left(\frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - 2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{2} + 4 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right)}{4} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} - 2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} + 2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}}$$

Simplificar

Tercera derivada [src]

/                                                                                   2                                                                                           /                                                                                      3                                                         2                                                                                       /                                                                                                       2                                                   \                                                                                                2                    3                                                                                                                  \                                                                        \                                      
|  /                                         /       2/x\\                         \                                                                                            |     /                                         /       2/x\\                         \                                             /       2/x\\      /                                         /       2/x\\                         \ |                             /       2/x\\                                                /       2/x\\                   2                                |                                          2                                        /       2/x\\        /       2/x\\                                               3                          2                                        |                                                                        |                                      
|  |                                       x*|1 + tan |-||     /       2   \       |                                                                                            |     |                                       x*|1 + tan |-||     /       2   \       |                                           6*|1 + tan |-||      |                                       x*|1 + tan |-||     /       2   \       | |                           4*|1 + tan |-||                                              x*|1 + tan |-||      /       2   \             /       2   \       |                             /       2   \              /       2   \          4*x*|1 + tan |-||    2*x*|1 + tan |-||                                  /       2   \              /       2   \                                         |                                                                        |                                      
|  |     /   /x\\                            \        \2//   2*\1 + tan (x)/*cos(x)|                                                                                            |     |     /   /x\\                            \        \2//   2*\1 + tan (x)/*cos(x)|          2/x\      /       2   \            \        \2//      |     /   /x\\                            \        \2//   2*\1 + tan (x)/*cos(x)| |    /       2   \            \        \2//       /       2/x\\                            \        \2//    4*\1 + tan (x)/ *cos(x)   8*\1 + tan (x)/*sin(x)|                          32*\1 + tan (x)/ *cos(x)   24*\1 + tan (x)/*cos(x)       \        \2//        \        \2//        /       2/x\\    /x\   16*\1 + tan (x)/ *cos(x)   24*\1 + tan (x)/ *sin(x)      /       2   \              |                                                                        |                                      
|3*|2*log|tan|-|| - 2*log(tan(x))*sin(x) + --------------- + ----------------------|                                                                                          x*|12 + |2*log|tan|-|| - 2*log(tan(x))*sin(x) + --------------- + ----------------------|  + 12*tan |-| - 48*\1 + tan (x)/*sin(x) - ---------------- + 3*|2*log|tan|-|| - 2*log(tan(x))*sin(x) + --------------- + ----------------------|*|- 8*\1 + tan (x)/*cos(x) - --------------- - 2*x*|1 + tan |-|| + 4*cos(x)*log(tan(x)) + ---------------- + ----------------------- + ----------------------| + 8*log(tan(x))*sin(x) - ------------------------ - ----------------------- - ------------------ + ------------------ + 4*x*|1 + tan |-||*tan|-| + ------------------------ + ------------------------ + 32*\1 + tan (x)/*cos(x)*tan(x)|                                                                       2|                                      
|  |     \   \2//                                  /x\               tan(x)        |                               /       2/x\\                              /       2/x\\     |     |     \   \2//                                  /x\               tan(x)        |           \2/                                    2/x\          |     \   \2//                                  /x\               tan(x)        | |                                   /x\           \        \2//                                 2/x\                   2                      tan(x)        |                                   tan(x)                     tan(x)                    /x\                 3/x\             \        \2//    \2/              3                          2                                             |                  2                                       /       2/x\\ |         /   /x\\                     
|  |                                            tan|-|                             |                             3*|1 + tan |-||                          3*x*|1 + tan |-||     |     |                                            tan|-|                             |                                               tan |-|          |                                            tan|-|                             | |                                tan|-|                                                      tan |-|                tan (x)                                 |                                                                                     tan|-|              tan |-|                                            tan (x)                    tan (x)                                          |     /       2   \             /       2   \          3*x*|1 + tan |-|| |  - x*log|tan|-|| - cos(x)*log(tan(x))
|  \                                               \2/                             /      /       2   \            \        \2//                              \        \2//     \     \                                               \2/                             /                                                   \2/          \                                               \2/                             / \                                   \2/                                                          \2/                                                        /                                                                                        \2/                  \2/                                                                                                                        /   3*\1 + tan (x)/ *cos(x)   6*\1 + tan (x)/*sin(x)       \        \2// |         \   \2//                     
|------------------------------------------------------------------------------------ - 6*\1 + tan (x)/*cos(x) - --------------- + 3*cos(x)*log(tan(x)) - ----------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- + ---------------------- + ------------------|*e                                    
|                                         4                                                                              /x\                                      2                                                                                                                                                                                                                                                                                                                                   8                                                                                                                                                                                                                                                                                                                                      2                      tan(x)                    2/x\     |                                      
|                                                                                                                     tan|-|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              tan (x)                                        4*tan |-|     |                                      
\                                                                                                                        \2/                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \2/     /

$$\left(\frac{3 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 \tan^{2}{\left(\frac{x}{2} \right)}} - \frac{3 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{2} - \frac{x \left(\frac{2 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{3}}{\tan^{3}{\left(\frac{x}{2} \right)}} - \frac{4 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\tan{\left(\frac{x}{2} \right)}} + 4 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} - \frac{6 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\tan^{2}{\left(\frac{x}{2} \right)}} + \frac{16 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \cos{\left(x \right)}}{\tan^{3}{\left(x \right)}} + \frac{24 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan^{2}{\left(x \right)}} - \frac{32 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan{\left(x \right)}} - 48 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} + 32 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} \tan{\left(x \right)} - \frac{24 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + \left(\frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - 2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{3} + 3 \left(\frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - 2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right) \left(\frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\tan^{2}{\left(\frac{x}{2} \right)}} - 2 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) - \frac{4 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(x \right)}} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} - 8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} + 4 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) + 8 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + 12 \tan^{2}{\left(\frac{x}{2} \right)} + 12\right)}{8} - \frac{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} - 6 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} + \frac{3 \left(\frac{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(\frac{x}{2} \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - 2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{2}}{4} + 3 \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) e^{- x \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}}$$

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Derivada de x*exp(-cos(x)(ln(tg(x)))-ln(tg(x/2))x)

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Derivada de x*exp(-cos(x)(ln(tg(x)))-ln(tg(x/2))x)

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