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Derivada de:
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Expresiones idénticas
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xexp(ln((2+tgx)/(2-tgx))-x)
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x*exp(ln((2+tgx) dividir por (2-tgx))-x)
Expresiones semejantes
x*exp(ln((2+tgx)/(2-tgx))+x)
x*exp(ln((2+tgx)/(2+tgx))-x)
x*exp(ln((2-tgx)/(2-tgx))-x)
Expresiones con funciones
ln
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ln^3(x^2+1)
ln(1+|x|)

Derivada de la función/ x*exp(ln((2+tgx)/(2-tgx))-x)

Derivada de x*exp(ln((2+tgx)/(2-tgx))-x)

Solución

Ha introducido [src]

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

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

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

$\frac{\left(5 x \tan^{2}{\left(x \right)} - \tan^{2}{\left(x \right)} + 4\right) e^{- x}}{\left(\tan{\left(x \right)} - 2\right)^{2}}$

Respuesta:

$\frac{\left(5 x \tan^{2}{\left(x \right)} - \tan^{2}{\left(x \right)} + 4\right) e^{- x}}{\left(\tan{\left(x \right)} - 2\right)^{2}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

/    /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        /                              /       2   \ /     2 + tan(x)\   /       2   \ /     2 + tan(x)\                                                       \                  /                              /       2   \ /     2 + tan(x)\   /       2   \ /     2 + tan(x)\                                                       \                                                                     /                              /       2   \ /     2 + tan(x)\   /       2   \ /     2 + tan(x)\                                                       \\                                                                                                                                                                                                                                                                          \    
|    |                                                                                                                                                                                                                                                                                                                                                                                                          /                                                                                                                    /         2      /       2   \                                            \                                            /         2      /       2   \                                            \                                                                                                                                                                                                                    \                2 |              /       2   \   \1 + tan (x)/*|1 - -----------|   \1 + tan (x)/*|1 - -----------|     /       2   \                                     |                2 |              /       2   \   \1 + tan (x)/*|1 - -----------|   \1 + tan (x)/*|1 - -----------|     /       2   \                                     |                 /              /       2   \                      \ |              /       2   \   \1 + tan (x)/*|1 - -----------|   \1 + tan (x)/*|1 - -----------|     /       2   \                                     ||                                                                                                                                                                                                                                                                          |    
|    |                                                                                                                                                                                                                                                                                                                                                                                                          |                                                                              2                       /       2   \ |  1 + tan (x)   \1 + tan (x)/*(2 + tan(x))   (2 + tan(x))*tan(x)         |                              /       2   \ |  1 + tan (x)   \1 + tan (x)/*(2 + tan(x))   (2 + tan(x))*tan(x)         |                                                                         2                                                                                                                                          |   /       2   \  |            2*\1 + tan (x)/                 \    -2 + tan(x)/                 \    -2 + tan(x)/   2*\1 + tan (x)/*(2 + tan(x))   2*(2 + tan(x))*tan(x)|   /       2   \  |            2*\1 + tan (x)/                 \    -2 + tan(x)/                 \    -2 + tan(x)/   2*\1 + tan (x)/*(2 + tan(x))   2*(2 + tan(x))*tan(x)|   /       2   \ |       2      \1 + tan (x)/*(2 + tan(x))         | |            2*\1 + tan (x)/                 \    -2 + tan(x)/                 \    -2 + tan(x)/   2*\1 + tan (x)/*(2 + tan(x))   2*(2 + tan(x))*tan(x)||                                                                                                                                                                                                                                                                          |    
|    |              /                              /       2   \ /     2 + tan(x)\   /       2   \ /     2 + tan(x)\                                                       \   /     /       2   \ /     2 + tan(x)\\ /                             2                                           2                                                                                           \                   |                                2                                /       2   \  /     2 + tan(x)\   2*\1 + tan (x)/*|- ----------- + -------------------------- - ------------------- + tan(x)|                            2*\1 + tan (x)/*|- ----------- + -------------------------- - ------------------- + tan(x)|                  2                                         /       2   \  /     2 + tan(x)\   /       2   \ /     2 + tan(x)\          /       2   \ /     2 + tan(x)\                                             |   \1 + tan (x)/ *|-2*tan(x) + --------------- + ------------------------------- - ------------------------------- - ---------------------------- + ---------------------|   \1 + tan (x)/ *|-2*tan(x) + --------------- + ------------------------------- - ------------------------------- - ---------------------------- + ---------------------|   \1 + tan (x)/*|1 - tan (x) + -------------------------- + tan(x)|*|-2*tan(x) + --------------- + ------------------------------- - ------------------------------- - ---------------------------- + ---------------------||                   /                              /       2   \ /     2 + tan(x)\   /       2   \ /     2 + tan(x)\                                                       \     /     /       2   \ /     2 + tan(x)\\                                                    |    
|    |              |              /       2   \   \1 + tan (x)/*|1 - -----------|   \1 + tan (x)/*|1 - -----------|     /       2   \                                     |   |     \1 + tan (x)/*|1 - -----------|| |                /       2   \                               /       2   \                   /       2   \                  /       2   \                             |                   |                   /       2   \    /       2   \                \1 + tan (x)/ *|1 - -----------|                   |  -2 + tan(x)                      2             -2 + tan(x)             |        2                                   |  -2 + tan(x)                      2             -2 + tan(x)             |     /       2   \                   /       2   \          \1 + tan (x)/ *|1 - -----------|   \1 + tan (x)/*|1 - -----------|*tan(x)   \1 + tan (x)/*|1 - -----------|*tan(x)     /       2   \                    |                  |              -2 + tan(x)                2 + tan(x)                       -2 + tan(x)                                 2               -2 + tan(x)     |                  |              -2 + tan(x)                2 + tan(x)                       -2 + tan(x)                                 2               -2 + tan(x)     |                 \                     -2 + tan(x)                 / |              -2 + tan(x)                2 + tan(x)                       -2 + tan(x)                                 2               -2 + tan(x)     ||                   |              /       2   \   \1 + tan (x)/*|1 - -----------|   \1 + tan (x)/*|1 - -----------|     /       2   \                                     |     |     \1 + tan (x)/*|1 - -----------|| /              /       2   \                      \|    
|    |/       2   \ |            2*\1 + tan (x)/                 \    -2 + tan(x)/                 \    -2 + tan(x)/   2*\1 + tan (x)/*(2 + tan(x))   2*(2 + tan(x))*tan(x)|   |                   \    -2 + tan(x)/| |       2      2*\1 + tan (x)/      /       2   \          2*\1 + tan (x)/ *(2 + tan(x))   2*\1 + tan (x)/*(2 + tan(x))   2*\1 + tan (x)/*(2 + tan(x))*tan(x)         |     /       2   \ |          2      3*\1 + tan (x)/    \1 + tan (x)/*(2 + tan(x))                  \    -2 + tan(x)/                   \                      (-2 + tan(x))                                      /   2*tan (x)*(2 + tan(x))                   \                      (-2 + tan(x))                                      /   3*\1 + tan (x)/ *(2 + tan(x))   6*\1 + tan (x)/*tan(x)                  \    -2 + tan(x)/                 \    -2 + tan(x)/                        \    -2 + tan(x)/          6*\1 + tan (x)/*(2 + tan(x))*tan(x)|                  \                                                                                                         (-2 + tan(x))                                /                  \                                                                                                         (-2 + tan(x))                                /                                                                     \                                                                                                         (-2 + tan(x))                                /|     /       2   \ |            2*\1 + tan (x)/                 \    -2 + tan(x)/                 \    -2 + tan(x)/   2*\1 + tan (x)/*(2 + tan(x))   2*(2 + tan(x))*tan(x)|     |                   \    -2 + tan(x)/| |       2      \1 + tan (x)/*(2 + tan(x))         ||  -x
|- x*|\1 + tan (x)/*|-2*tan(x) + --------------- + ------------------------------- - ------------------------------- - ---------------------------- + ---------------------| + |-1 + -------------------------------|*|- 2*tan (x) - ---------------- + 2*\1 + tan (x)/*tan(x) + ----------------------------- + ---------------------------- - ----------------------------------- + tan(x)| - 2*\1 + tan (x)/*|-1 - 3*tan (x) - ---------------- + -------------------------- - -------------------------------- - ------------------------------------------------------------------------------------------- + ---------------------- + ------------------------------------------------------------------------------------------- + ----------------------------- + ---------------------- + -------------------------------- + -------------------------------------- - -------------------------------------- - -----------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 3*\1 + tan (x)/*|-2*tan(x) + --------------- + ------------------------------- - ------------------------------- - ---------------------------- + ---------------------| + 3*|-1 + -------------------------------|*|1 - tan (x) + -------------------------- + tan(x)||*e  
|    |              |              -2 + tan(x)                2 + tan(x)                       -2 + tan(x)                                 2               -2 + tan(x)     |   \                2 + tan(x)          / |                -2 + tan(x)                                                    2                  -2 + tan(x)                        -2 + tan(x)                     |                   |                               2           -2 + tan(x)                                2                                                     -2 + tan(x)                                                -2 + tan(x)                                                  2 + tan(x)                                                                3               -2 + tan(x)            (-2 + tan(x))*(2 + tan(x))                    2 + tan(x)                              -2 + tan(x)                                         2          |                                                                                 -2 + tan(x)                                                                                                                                                                2 + tan(x)                                                                                                                                                                                         2 + tan(x)                                                                                                        |                   |              -2 + tan(x)                2 + tan(x)                       -2 + tan(x)                                 2               -2 + tan(x)     |     \                2 + tan(x)          / \                     -2 + tan(x)                 /|    
\    \              \                                                                                                         (-2 + tan(x))                                /                                          \                                                                  (-2 + tan(x))                                                                                      /                   \                  (-2 + tan(x))                                           (2 + tan(x))                                                                                                                                                                                                                                           (-2 + tan(x))                                                                                                                                                                    (-2 + tan(x))           /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                   \                                                                                                         (-2 + tan(x))                                /                                                                                               /    
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         -2 + tan(x)

$$\frac{\left(- x \left(\left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - 1\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - 2 \tan^{2}{\left(x \right)} + \tan{\left(x \right)} - \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right) + \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - 2 \tan{\left(x \right)} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right) - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\tan{\left(x \right)} + 2} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(\tan{\left(x \right)} + 2\right)^{2}} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} + 2\right)} - 3 \tan^{2}{\left(x \right)} - 1 + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan{\left(x \right)} - \frac{\left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} - \frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)} - 2} + \frac{\left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right)}{\tan{\left(x \right)} + 2} + \frac{\left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \tan^{2}{\left(x \right)}}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan{\left(x \right)} - \frac{\left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} - \frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)} - 2} + \frac{\left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right)}{\tan{\left(x \right)} - 2} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} - \frac{6 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\left(\tan{\left(x \right)} - 2\right)^{2}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(\tan{\left(x \right)} - 2\right)^{2}} + \frac{3 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(\tan{\left(x \right)} - 2\right)^{3}}\right) - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - 2 \tan{\left(x \right)} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right)}{\tan{\left(x \right)} + 2} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(- \tan^{2}{\left(x \right)} + \tan{\left(x \right)} + 1 + \frac{\left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2}\right) \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - 2 \tan{\left(x \right)} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right)}{\tan{\left(x \right)} + 2} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - 2 \tan{\left(x \right)} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right)}{\tan{\left(x \right)} - 2}\right) + 3 \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - 1\right) \left(- \tan^{2}{\left(x \right)} + \tan{\left(x \right)} + 1 + \frac{\left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2}\right) + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} + 2} - \frac{\left(1 - \frac{\tan{\left(x \right)} + 2}{\tan{\left(x \right)} - 2}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - 2 \tan{\left(x \right)} + \frac{2 \left(\tan{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan{\left(x \right)} - 2} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)} - 2} - \frac{2 \left(\tan{\left(x \right)} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(\tan{\left(x \right)} - 2\right)^{2}}\right)\right) e^{- x}}{\tan{\left(x \right)} - 2}$$

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Derivada de x*exp(ln((2+tgx)/(2-tgx))-x)

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Derivada de x*exp(ln((2+tgx)/(2-tgx))-x)

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