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Derivada de:
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Expresiones idénticas
x*exsin(cos^ dos (tan^ tres (x)))+exp(uno /x)p(-x)
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x*exsin(cos2(tan3(x)))+exp(1/x)p(-x)
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x*exsin(cos²(tan³(x)))+exp(1/x)p(-x)
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xexsin(cos^2(tan^3(x)))+exp(1/x)p(-x)
xexsin(cos2(tan3(x)))+exp(1/x)p(-x)
xexsincos2tan3x+exp1/xp-x
xexsincos^2tan^3x+exp1/xp-x
x*exsin(cos^2(tan^3(x)))+exp(1 dividir por x)p(-x)
Expresiones semejantes
x*exsin(cos^2(tan^3(x)))-exp(1/x)p(-x)
x*exsin(cos^2(tan^3(x)))+exp(1/x)p(x)

Derivada de la función/ x*exsin(cos^2(tan^3(x)))+exp(1/x)p(-x)

Derivada de x*exsin(cos^2(tan^3(x)))+exp(1/x)p(-x)

Solución

Ha introducido [src]

                           1       
                           -       
   x    /   2/   3   \\    x       
x*E *sin\cos \tan (x)// + e *p*(-x)

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

(x*E^x)*sin(cos(tan(x)^3)^2) + (exp(1/x)*p)*(-x)

Solución detallada

diferenciamos $- x p e^{\frac{1}{x}} + e^{x} x \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)}$ miembro por miembro:
1. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = e^{x} x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
  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 $\frac{d}{d x} f{\left(x \right)}$ :
    1. Según el principio, aplicamos: $x$ tenemos $1$
    $g{\left(x \right)} = e^{x}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. Derivado $e^{x}$ es.
    Como resultado de: $e^{x} + x e^{x}$
  $g{\left(x \right)} = \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
  1. Sustituimos $u = \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)}$ .
  2. La derivada del seno es igual al coseno:
    
    $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)}$ :
    1. Sustituimos $u = \cos{\left(\tan^{3}{\left(x \right)} \right)}$ .
    2. Según el principio, aplicamos: $u^{2}$ tenemos $2 u$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \cos{\left(\tan^{3}{\left(x \right)} \right)}$ :
      1. Sustituimos $u = \tan^{3}{\left(x \right)}$ .
      2. La derivada del coseno es igual a menos el seno:
        
        $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
      3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \tan^{3}{\left(x \right)}$ :
        
        Sustituimos $u = \tan{\left(x \right)}$ .
        
        Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
        
        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:
        
        $\frac{3 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
        
        Como resultado de la secuencia de reglas:
        
        $- \frac{3 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
      Como resultado de la secuencia de reglas:
      
      $- \frac{6 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
    Como resultado de la secuencia de reglas:
    
    $- \frac{6 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
  Como resultado de: $- \frac{6 x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \left(e^{x} + x e^{x}\right) \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)}$
2. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = p e^{\frac{1}{x}}$ ; 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.
    1. Sustituimos $u = \frac{1}{x}$ .
    2. Derivado $e^{u}$ es.
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{1}{x}$ :
      1. Según el principio, aplicamos: $\frac{1}{x}$ tenemos $- \frac{1}{x^{2}}$
      Como resultado de la secuencia de reglas:
      
      $- \frac{e^{\frac{1}{x}}}{x^{2}}$
    Entonces, como resultado: $- \frac{p e^{\frac{1}{x}}}{x^{2}}$
  $g{\left(x \right)} = - x$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
  1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
    1. Según el principio, aplicamos: $x$ tenemos $1$
    Entonces, como resultado: $-1$
  Como resultado de: $- p e^{\frac{1}{x}} + \frac{p e^{\frac{1}{x}}}{x}$
Como resultado de: $- p e^{\frac{1}{x}} + \frac{p e^{\frac{1}{x}}}{x} - \frac{6 x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \left(e^{x} + x e^{x}\right) \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)}$
Simplificamos:

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

Respuesta:

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

Primera derivada [src]

                                           1                                                                              
                                    1      -                                                                              
                                    -      x                                                                              
/ x      x\    /   2/   3   \\      x   p*e           2    /         2   \    /   2/   3   \\    /   3   \  x    /   3   \
\E  + x*e /*sin\cos \tan (x)// - p*e  + ---- - 2*x*tan (x)*\3 + 3*tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/
                                         x

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

Simplificar

Segunda derivada [src]

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         x    /   2/   3   \\   p*e         /       2   \     2/   3   \    4       /   2/   3   \\  x        2    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \        /       2   \     2/   3   \    4       /   2/   3   \\  x        /       2   \     2/   3   \    2/   3   \    4     x    /   2/   3   \\        /       2   \     /   2/   3   \\    /   3   \  x    /   3   \                  3    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \          2    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \        2            /       2   \    /   2/   3   \\    /   3   \  x    /   3   \
(2 + x)*e *sin\cos \tan (x)// - ---- - 18*x*\1 + tan (x)/ *cos \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 6*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ + 18*x*\1 + tan (x)/ *sin \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 36*x*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*e *sin\cos \tan (x)// - 12*x*\1 + tan (x)/ *cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/*tan(x) - 12*x*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 6*x*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 6*tan (x)*(1 + x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/
                                  3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
                                 x

$$- \frac{p e^{\frac{1}{x}}}{x^{3}} - 36 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} + 18 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \tan^{4}{\left(x \right)} - 12 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan{\left(x \right)} - 18 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} - 12 x \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 6 x \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 6 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)} + \left(x + 2\right) e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} - 6 \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}$$

Simplificar

Tercera derivada [src]

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   x                                        x                   2                                                               2                                                                  2                                                                  3                                                               2                                                                               2                                                               2                                                                                                                                                     2                                                                         3                                                                                                                                              2                                                                         2                                                                  2                                                                  3                                                                  3                                                                               2                                                                                3                                                                               2                                                                             2                                                                             2                                                                                       2                                                                                                                                                                                                                                    2                                                                                                                                                                                                                                                                                                                                       3                                                                                3                                                                              3                                                         
p*e             x    /   2/   3   \\   3*p*e       /       2   \     2/   3   \    4       /   2/   3   \\  x      /       2   \     2/   3   \    4       /   2/   3   \\  x         /       2   \     2/   3   \    5       /   2/   3   \\  x         /       2   \     2/   3   \    3       /   2/   3   \\  x      /       2   \     2/   3   \    2/   3   \    4     x    /   2/   3   \\        /       2   \     2/   3   \    4       /   2/   3   \\  x      /       2   \     /   2/   3   \\    /   3   \  x    /   3   \                3    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \      /       2   \     2/   3   \    4               /   2/   3   \\  x        /       2   \     /   2/   3   \\    /   3   \  x    /   3   \         2    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \      /       2   \     2/   3   \    4               /   2/   3   \\  x        /       2   \     2/   3   \    4       /   2/   3   \\  x         /       2   \     2/   3   \    5       /   2/   3   \\  x         /       2   \     2/   3   \    3       /   2/   3   \\  x         /       2   \     3/   3   \    6     x    /   2/   3   \\    /   3   \         /       2   \     2/   3   \    2/   3   \    5     x    /   2/   3   \\         /       2   \     2/   3   \    2/   3   \    3     x    /   2/   3   \\        /       2   \     2       /   2/   3   \\    /   3   \  x    /   3   \        /       2   \     2/   3   \    2/   3   \    4     x    /   2/   3   \\      /       2   \     2/   3   \    2/   3   \    4             x    /   2/   3   \\        /       2   \     /   2/   3   \\    /   3   \  x    /   3   \                  3    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \           4    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \      /       2   \             /   2/   3   \\    /   3   \  x    /   3   \                2    /       2   \            /   2/   3   \\    /   3   \  x    /   3   \         3            /       2   \    /   2/   3   \\    /   3   \  x    /   3   \          2    /       2   \    /   2/   3   \\    /   3   \  x    /   3   \         /       2   \     3/   3   \    3/   3   \    6       /   2/   3   \\  x         /       2   \     6       /   2/   3   \\    /   3   \  x    /   3   \         /       2   \     3/   3   \    6       /   3   \  x    /   2/   3   \\
---- + (3 + x)*e *sin\cos \tan (x)// + ------ - 36*\1 + tan (x)/ *cos \tan (x)/*tan (x)*cos\cos \tan (x)//*e  + 36*\1 + tan (x)/ *sin \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 108*x*\1 + tan (x)/ *cos \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 108*x*\1 + tan (x)/ *cos \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 72*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*e *sin\cos \tan (x)// - 36*x*\1 + tan (x)/ *cos \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 24*\1 + tan (x)/ *cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/*tan(x) - 24*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 18*\1 + tan (x)/ *cos \tan (x)/*tan (x)*(1 + x)*cos\cos \tan (x)//*e  - 12*x*\1 + tan (x)/ *cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 12*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ + 18*\1 + tan (x)/ *sin \tan (x)/*tan (x)*(1 + x)*cos\cos \tan (x)//*e  + 36*x*\1 + tan (x)/ *sin \tan (x)/*tan (x)*cos\cos \tan (x)//*e  + 108*x*\1 + tan (x)/ *sin \tan (x)/*tan (x)*cos\cos \tan (x)//*e  + 108*x*\1 + tan (x)/ *sin \tan (x)/*tan (x)*cos\cos \tan (x)//*e  - 324*x*\1 + tan (x)/ *cos \tan (x)/*tan (x)*e *sin\cos \tan (x)//*sin\tan (x)/ - 216*x*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*e *sin\cos \tan (x)// - 216*x*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*e *sin\cos \tan (x)// - 84*x*\1 + tan (x)/ *tan (x)*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 72*x*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*e *sin\cos \tan (x)// - 36*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*(1 + x)*e *sin\cos \tan (x)// - 24*x*\1 + tan (x)/ *cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/*tan(x) - 24*x*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 24*x*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 12*\1 + tan (x)/ *(1 + x)*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/*tan(x) - 12*tan (x)*\1 + tan (x)/*(2 + x)*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 12*tan (x)*(1 + x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ - 6*x*tan (x)*\1 + tan (x)/*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ + 216*x*\1 + tan (x)/ *cos \tan (x)/*sin \tan (x)/*tan (x)*cos\cos \tan (x)//*e  + 216*x*\1 + tan (x)/ *tan (x)*cos\cos \tan (x)//*cos\tan (x)/*e *sin\tan (x)/ + 324*x*\1 + tan (x)/ *sin \tan (x)/*tan (x)*cos\tan (x)/*e *sin\cos \tan (x)//
  5                                       4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
 x                                       x

$$\frac{3 p e^{\frac{1}{x}}}{x^{4}} + \frac{p e^{\frac{1}{x}}}{x^{5}} + 324 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{3}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{6}{\left(x \right)} - 216 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 324 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos^{3}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{6}{\left(x \right)} + 216 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin^{3}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{3}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{6}{\left(x \right)} + 108 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \tan^{3}{\left(x \right)} + 216 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{6}{\left(x \right)} - 12 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} - 108 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3} e^{x} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 216 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{5}{\left(x \right)} - 72 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} + 108 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \tan^{5}{\left(x \right)} + 36 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \tan^{4}{\left(x \right)} - 84 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 24 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan{\left(x \right)} - 108 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{5}{\left(x \right)} - 36 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} - 24 x \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} - 24 x \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 6 x \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 36 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} + 18 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \tan^{4}{\left(x \right)} - 12 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan{\left(x \right)} - 18 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} - 12 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 12 \left(x + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)} + \left(x + 3\right) e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} - 72 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} + 36 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin^{2}{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \tan^{4}{\left(x \right)} - 24 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan{\left(x \right)} - 36 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} e^{x} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \tan^{4}{\left(x \right)} - 24 \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 12 \left(\tan^{2}{\left(x \right)} + 1\right) e^{x} \sin{\left(\tan^{3}{\left(x \right)} \right)} \cos{\left(\cos^{2}{\left(\tan^{3}{\left(x \right)} \right)} \right)} \cos{\left(\tan^{3}{\left(x \right)} \right)} \tan^{2}{\left(x \right)}$$

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Derivada de x*exsin(cos^2(tan^3(x)))+exp(1/x)p(-x)

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