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Expresiones idénticas
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Expresiones semejantes
е^(-x^2)*cos(2^sinx)^2-x^tgx
е^(x^2)*cos(2^sinx)^2+x^tgx
Expresiones con funciones
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Derivada de la función/ е^(-x^2)*cos(2^sinx)^2+x^tgx

Derivada de е^(-x^2)*cos(2^sinx)^2+x^tgx

Solución

Ha introducido [src]

   2                        
 -x     2/ sin(x)\    tan(x)
E   *cos \2      / + x

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

E^(-x^2)*cos(2^sin(x))^2 + x^tan(x)

Solución detallada

diferenciamos $x^{\tan{\left(x \right)}} + e^{- x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)}$ miembro por miembro:
1. Se aplica la regla de la derivada parcial:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)}$ y $g{\left(x \right)} = e^{x^{2}}$ .
  
  Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
  1. Sustituimos $u = \cos{\left(2^{\sin{\left(x \right)}} \right)}$ .
  2. Según el principio, aplicamos: $u^{2}$ tenemos $2 u$
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \cos{\left(2^{\sin{\left(x \right)}} \right)}$ :
    1. Sustituimos $u = 2^{\sin{\left(x \right)}}$ .
    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 $\frac{d}{d x} 2^{\sin{\left(x \right)}}$ :
      1. Sustituimos $u = \sin{\left(x \right)}$ .
      2. $\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}$
      3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \sin{\left(x \right)}$ :
        
        La derivada del seno es igual al coseno:
        
        $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
        
        Como resultado de la secuencia de reglas:
        
        $2^{\sin{\left(x \right)}} \log{\left(2 \right)} \cos{\left(x \right)}$
      Como resultado de la secuencia de reglas:
      
      $- 2^{\sin{\left(x \right)}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)}$
    Como resultado de la secuencia de reglas:
    
    $- 2 \cdot 2^{\sin{\left(x \right)}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)}$
  Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
  1. Sustituimos $u = x^{2}$ .
  2. Derivado $e^{u}$ es.
  3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} x^{2}$ :
    1. Según el principio, aplicamos: $x^{2}$ tenemos $2 x$
    Como resultado de la secuencia de reglas:
    
    $2 x e^{x^{2}}$
  Ahora aplicamos la regla de la derivada de una divesión:
  
  $\left(- 2 \cdot 2^{\sin{\left(x \right)}} e^{x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 2 x e^{x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)}\right) e^{- 2 x^{2}}$
2. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$
Como resultado de: $\left(- 2 \cdot 2^{\sin{\left(x \right)}} e^{x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 2 x e^{x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)}\right) e^{- 2 x^{2}} + \left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$
Simplificamos:

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

                                       3           /    /       2   \                             2                                             /       2   \       \                         2                                             /             /       2   \                                \                         2                                                2                                                2                                                   2                                               2                                                    2                                                            2                                                      2                                                                2                                     2                                                            2                                                    2                                                                       2                                                                    2             
 tan(x) /tan(x)   /       2   \       \     tan(x) |  3*\1 + tan (x)/   2*tan(x)     /       2   \                2    /       2   \          6*\1 + tan (x)/*tan(x)|      3    2/ sin(x)\  -x       tan(x) /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |           2/ sin(x)\  -x       2*sin(x)    3       2/ sin(x)\    3     -x       2*sin(x)    3       3       2/ sin(x)\  -x          2*sin(x)    2       2       2/ sin(x)\  -x       2*sin(x)    2       2/ sin(x)\         -x              sin(x)    3       3       / sin(x)\  -x     / sin(x)\      2*sin(x)    2/ sin(x)\    2            -x              3*sin(x)    3       3       / sin(x)\  -x     / sin(x)\         2*sin(x)    2       2/ sin(x)\    2     -x        sin(x)           / sin(x)\  -x            / sin(x)\       sin(x)  2           / sin(x)\  -x            / sin(x)\         sin(x)    / sin(x)\  -x                   / sin(x)\      sin(x)    2              / sin(x)\  -x            / sin(x)\         sin(x)    2       2       / sin(x)\  -x     / sin(x)\
x      *|------ + \1 + tan (x)/*log(x)|  + x      *|- --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------| - 8*x *cos \2      /*e    + 3*x      *|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + 12*x*cos \2      /*e    - 6*2        *cos (x)*cos \2      /*log (2)*e    + 6*2        *cos (x)*log (2)*sin \2      /*e    - 12*x*2        *cos (x)*log (2)*sin \2      /*e    - 6*2        *log (2)*sin \2      /*cos(x)*e   *sin(x) - 2*2      *cos (x)*log (2)*cos\2      /*e   *sin\2      / + 6*2        *cos \2      /*log (2)*cos(x)*e   *sin(x) + 8*2        *cos (x)*log (2)*cos\2      /*e   *sin\2      / + 12*x*2        *cos (x)*cos \2      /*log (2)*e    + 14*2      *cos(x)*cos\2      /*e   *log(2)*sin\2      / - 24*2      *x *cos(x)*cos\2      /*e   *log(2)*sin\2      / - 12*x*2      *cos\2      /*e   *log(2)*sin(x)*sin\2      / + 6*2      *log (2)*cos(x)*cos\2      /*e   *sin(x)*sin\2      / + 12*x*2      *cos (x)*log (2)*cos\2      /*e   *sin\2      /
        \  x                          /            |          2             3                                                                           x           |                                       \  x                          / |     2            x                                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
                                                   \         x             x                                                                                        /                                                                       \    x                                                     /

$$8 \cdot 2^{3 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{3} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos^{3}{\left(x \right)} - 12 \cdot 2^{2 \sin{\left(x \right)}} x e^{- x^{2}} \log{\left(2 \right)}^{2} \sin^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos^{2}{\left(x \right)} + 12 \cdot 2^{2 \sin{\left(x \right)}} x e^{- x^{2}} \log{\left(2 \right)}^{2} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos^{2}{\left(x \right)} - 6 \cdot 2^{2 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{2} \sin^{2}{\left(2^{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} \cos{\left(x \right)} + 6 \cdot 2^{2 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{3} \sin^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos^{3}{\left(x \right)} + 6 \cdot 2^{2 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{2} \sin{\left(x \right)} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 6 \cdot 2^{2 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{3} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos^{3}{\left(x \right)} - 24 \cdot 2^{\sin{\left(x \right)}} x^{2} e^{- x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 12 \cdot 2^{\sin{\left(x \right)}} x e^{- x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} + 12 \cdot 2^{\sin{\left(x \right)}} x e^{- x^{2}} \log{\left(2 \right)}^{2} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos^{2}{\left(x \right)} + 6 \cdot 2^{\sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{2} \sin{\left(2^{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 2 \cdot 2^{\sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{3} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos^{3}{\left(x \right)} + 14 \cdot 2^{\sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 8 x^{3} e^{- x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} + 12 x e^{- x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} + x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + x^{\tan{\left(x \right)}} \left(2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}\right)$$

Simplificar

Gráfico

Derivada de е^(-x^2)*cos(2^sinx)^2+x^tgx

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de е^(-x^2)*cos(2^sinx)^2+x^tgx

Gráfico:

Definida a trozos:

Solución