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е^(-x^2)*cos(2^sinx)^2+x^tgx

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

Función f() - derivada -er orden en el punto
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Gráfico:

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Definida a trozos:

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
  1. diferenciamos miembro por miembro:

    1. Se aplica la regla de la derivada parcial:

      y .

      Para calcular :

      1. Sustituimos .

      2. Según el principio, aplicamos: tenemos

      3. Luego se aplica una cadena de reglas. Multiplicamos por :

        1. Sustituimos .

        2. La derivada del coseno es igual a menos el seno:

        3. Luego se aplica una cadena de reglas. Multiplicamos por :

          1. Sustituimos .

          2. Luego se aplica una cadena de reglas. Multiplicamos por :

            1. La derivada del seno es igual al coseno:

            Como resultado de la secuencia de reglas:

          Como resultado de la secuencia de reglas:

        Como resultado de la secuencia de reglas:

      Para calcular :

      1. Sustituimos .

      2. Derivado es.

      3. Luego se aplica una cadena de reglas. Multiplicamos por :

        1. Según el principio, aplicamos: tenemos

        Como resultado de la secuencia de reglas:

      Ahora aplicamos la regla de la derivada de una divesión:

    2. No logro encontrar los pasos en la búsqueda de esta derivada.

      Perola derivada

    Como resultado de:

  2. Simplificamos:


Respuesta:

Gráfica
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                          /                                                                                  
$$- 2 \cdot 2^{\sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} - 2 x e^{- x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} + x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)$$
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                                                     /                                                                                                                                                                                                                                                                                                                                  
$$2 \cdot 2^{2 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{2} \sin^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos^{2}{\left(x \right)} - 2 \cdot 2^{2 \sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{2} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} \cos^{2}{\left(x \right)} + 8 \cdot 2^{\sin{\left(x \right)}} x e^{- x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(x \right)} + 2 \cdot 2^{\sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)} \sin{\left(2^{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} - 2 \cdot 2^{\sin{\left(x \right)}} e^{- x^{2}} \log{\left(2 \right)}^{2} \sin{\left(2^{\sin{\left(x \right)}} \right)} \cos{\left(2^{\sin{\left(x \right)}} \right)} \cos^{2}{\left(x \right)} + 4 x^{2} e^{- x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)} + x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + x^{\tan{\left(x \right)}} \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) - 2 e^{- x^{2}} \cos^{2}{\left(2^{\sin{\left(x \right)}} \right)}$$
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)$$
Gráfico
Derivada de е^(-x^2)*cos(2^sinx)^2+x^tgx