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Derivada de la función/ x*(tan(3*(x^4)))^sqrt(x+3)exp(-x)

Derivada de x(tan(3(x^4)))^sqrt(x+3)exp(-x)

Solución

Ha introducido [src]

               _______    
             \/ x + 3     
  /   /   4\\           -x
x*\tan\3*x //         *e

$$x \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)} e^{- x}$$

(x*tan(3*x^4)^(sqrt(x + 3)))*exp(-x)

Solución detallada

Se aplica la regla de la derivada parcial:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}$ y $g{\left(x \right)} = e^{x}$ .

Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
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 $1$
  $g{\left(x \right)} = \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
  1. No logro encontrar los pasos en la búsqueda de esta derivada.
    
    Perola derivada
    
    $\left(x + 3\right)^{\frac{\sqrt{x + 3}}{2}} \left(\log{\left(\sqrt{x + 3} \right)} + 1\right)$
  Como resultado de: $x \left(x + 3\right)^{\frac{\sqrt{x + 3}}{2}} \left(\log{\left(\sqrt{x + 3} \right)} + 1\right) + \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}$
Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
1. Derivado $e^{x}$ es.
Ahora aplicamos la regla de la derivada de una divesión:

$\left(- x e^{x} \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)} + \left(x \left(x + 3\right)^{\frac{\sqrt{x + 3}}{2}} \left(\log{\left(\sqrt{x + 3} \right)} + 1\right) + \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}\right) e^{x}\right) e^{- 2 x}$
Simplificamos:

$\left(x \left(x + 3\right)^{\frac{\sqrt{x + 3}}{2}} \left(\frac{\log{\left(x + 3 \right)}}{2} + 1\right) - x \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)} + \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}\right) e^{- x}$

Respuesta:

$\left(x \left(x + 3\right)^{\frac{\sqrt{x + 3}}{2}} \left(\frac{\log{\left(x + 3 \right)}}{2} + 1\right) - x \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)} + \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}\right) e^{- x}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

/             _______                  _______                                                    \                      _______    
|           \/ x + 3                 \/ x + 3  /   /   /   4\\       3   _______ /       2/   4\\\|                    \/ x + 3     
|/   /   4\\              /   /   4\\          |log\tan\3*x //   12*x *\/ x + 3 *\1 + tan \3*x //||  -x     /   /   4\\           -x
|\tan\3*x //          + x*\tan\3*x //         *|-------------- + --------------------------------||*e   - x*\tan\3*x //         *e  
|                                              |     _______                   /   4\            ||                                 
\                                              \ 2*\/ x + 3                 tan\3*x /            //

$$- x e^{- x} \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)} + \left(x \left(\frac{12 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{2 \sqrt{x + 3}}\right) \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)} + \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}\right) e^{- x}$$

Simplificar

Segunda derivada [src]

                     /                                                                                    /                                                   2                                                                                2                                                                       \                                   \    
                     |                                                                                    |/   /   /   4\\       3   _______ /       2/   4\\\       /   /   4\\                                             6 /       2/   4\\    _______       3 /       2/   4\\        2   _______ /       2/   4\\|                                   |    
                     |                                                                                    ||log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //|    log\tan\3*x //         6   _______ /       2/   4\\   576*x *\1 + tan \3*x // *\/ 3 + x    48*x *\1 + tan \3*x //   144*x *\/ 3 + x *\1 + tan \3*x //|                                   |    
             _______ |                                                                                  x*||-------------- + --------------------------------|  - -------------- + 1152*x *\/ 3 + x *\1 + tan \3*x // - ---------------------------------- + ---------------------- + ---------------------------------|                                   |    
           \/ 3 + x  |            /   /   4\\     /   /   /   4\\       3   _______ /       2/   4\\\     ||    _______                    /   4\            |             3/2                                                         2/   4\                  _______    /   4\                    /   4\            |       3   _______ /       2/   4\\|    
/   /   4\\          |         log\tan\3*x //     |log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //|     \\  \/ 3 + x                  tan\3*x /            /      (3 + x)                                                         tan \3*x /                \/ 3 + x *tan\3*x /                 tan\3*x /            /   24*x *\/ 3 + x *\1 + tan \3*x //|  -x
\tan\3*x //         *|-2 + x + -------------- - x*|-------------- + --------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------|*e  
                     |             _______        |    _______                    /   4\            |                                                                                                          4                                                                                                                         /   4\            |    
                     \           \/ 3 + x         \  \/ 3 + x                  tan\3*x /            /                                                                                                                                                                                                                                 tan\3*x /            /

$$\left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} - x \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right) + \frac{x \left(- \frac{576 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\tan^{2}{\left(3 x^{4} \right)}} + 1152 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right) + \frac{48 x^{3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\sqrt{x + 3} \tan{\left(3 x^{4} \right)}} + \frac{144 x^{2} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right)^{2} - \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\left(x + 3\right)^{\frac{3}{2}}}\right)}{4} + x - 2 + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right) e^{- x} \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}$$

Simplificar

Tercera derivada [src]

                     /                                                             2                          /                                                   2                                                                                2                                                                       \                        /                                                   3                                                                            /                                                                               2                                                                       \                                                                                             2                                      2                                     2                                                                                                                  3                                                          \                                                                                                                                                                                                                                   \    
                     |          /   /   /   4\\       3   _______ /       2/   4\\\                           |/   /   /   4\\       3   _______ /       2/   4\\\       /   /   4\\                                             6 /       2/   4\\    _______       3 /       2/   4\\        2   _______ /       2/   4\\|                        |/   /   /   4\\       3   _______ /       2/   4\\\         /   /   4\\     /   /   /   4\\       3   _______ /       2/   4\\\ |     /   /   4\\                                             6 /       2/   4\\    _______       3 /       2/   4\\        2   _______ /       2/   4\\|         6 /       2/   4\\                                                9 /       2/   4\\    _______          5 /       2/   4\\    _______         6 /       2/   4\\        3 /       2/   4\\        2 /       2/   4\\           _______ /       2/   4\\          9 /       2/   4\\    _______                                                |       /   /   /   4\\       3   _______ /       2/   4\\\                                                                                                                                                                         |    
                     |          |log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //|                           ||log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //|    log\tan\3*x //         6   _______ /       2/   4\\   576*x *\1 + tan \3*x // *\/ 3 + x    48*x *\1 + tan \3*x //   144*x *\/ 3 + x *\1 + tan \3*x //|                        ||log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //|    3*log\tan\3*x //     |log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //| |  log\tan\3*x //         6   _______ /       2/   4\\   576*x *\1 + tan \3*x // *\/ 3 + x    48*x *\1 + tan \3*x //   144*x *\/ 3 + x *\1 + tan \3*x //|   3456*x *\1 + tan \3*x //          5   _______ /       2/   4\\   55296*x *\1 + tan \3*x // *\/ 3 + x    10368*x *\1 + tan \3*x // *\/ 3 + x    1728*x *\1 + tan \3*x //    72*x *\1 + tan \3*x //   432*x *\1 + tan \3*x //   576*x*\/ 3 + x *\1 + tan \3*x //   27648*x *\1 + tan \3*x // *\/ 3 + x           9   _______ /       2/   4\\    /   4\|       |log\tan\3*x //   24*x *\/ 3 + x *\1 + tan \3*x //|                                                                                                                                                                         |    
             _______ |        3*|-------------- + --------------------------------|                       3*x*||-------------- + --------------------------------|  - -------------- + 1152*x *\/ 3 + x *\1 + tan \3*x // - ---------------------------------- + ---------------------- + ---------------------------------|                      x*||-------------- + --------------------------------|  + ---------------- + 3*|-------------- + --------------------------------|*|- -------------- + 1152*x *\/ 3 + x *\1 + tan \3*x // - ---------------------------------- + ---------------------- + ---------------------------------| + ------------------------ + 20736*x *\/ 3 + x *\1 + tan \3*x // - ------------------------------------ - ------------------------------------ - ------------------------- - ---------------------- + ----------------------- + -------------------------------- + ------------------------------------ + 55296*x *\/ 3 + x *\1 + tan \3*x //*tan\3*x /|   3*x*|-------------- + --------------------------------|                                                              2                                                                                                          |    
           \/ 3 + x  |          |    _______                    /   4\            |         /   /   4\\       ||    _______                    /   4\            |             3/2                                                         2/   4\                  _______    /   4\                    /   4\            |        /   /   4\\     ||    _______                    /   4\            |              5/2        |    _______                    /   4\            | |           3/2                                                         2/   4\                  _______    /   4\                    /   4\            |            _______                                                                 /   4\                                 2/   4\                     _______    2/   4\             3/2    /   4\        _______    /   4\                   /   4\                               3/   4\                                                             |       |    _______                    /   4\            |                                            6 /       2/   4\\    _______       3   _______ /       2/   4\\       3 /       2/   4\\        2   _______ /       2/   4\\|    
/   /   4\\          |          \  \/ 3 + x                  tan\3*x /            /    3*log\tan\3*x //       \\  \/ 3 + x                  tan\3*x /            /      (3 + x)                                                         tan \3*x /                \/ 3 + x *tan\3*x /                 tan\3*x /            /   3*log\tan\3*x //     \\  \/ 3 + x                  tan\3*x /            /       (3 + x)           \  \/ 3 + x                  tan\3*x /            / \    (3 + x)                                                         tan \3*x /                \/ 3 + x *tan\3*x /                 tan\3*x /            /          \/ 3 + x                                                               tan\3*x /                              tan \3*x /                   \/ 3 + x *tan \3*x /      (3 + x)   *tan\3*x /      \/ 3 + x *tan\3*x /                tan\3*x /                            tan \3*x /                                                             /       \  \/ 3 + x                  tan\3*x /            /        6   _______ /       2/   4\\   432*x *\1 + tan \3*x // *\/ 3 + x    72*x *\/ 3 + x *\1 + tan \3*x //   36*x *\1 + tan \3*x //   108*x *\/ 3 + x *\1 + tan \3*x //|  -x
\tan\3*x //         *|3 - x + ------------------------------------------------------ - ---------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------- + 864*x *\/ 3 + x *\1 + tan \3*x // - ---------------------------------- - -------------------------------- + ---------------------- + ---------------------------------|*e  
                     |                                  4                                   _______                                                                                                               4                                                                                                                       3/2                                                                                                                                                                                                                                                                                                                               8                                                                                                                                                                                                                                                                                                                                                        2                                                                                 2/   4\                             /   4\                  _______    /   4\                    /   4\            |    
                     \                                                                    \/ 3 + x                                                                                                                                                                                                                               4*(3 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          tan \3*x /                          tan\3*x /                \/ 3 + x *tan\3*x /                 tan\3*x /            /

$$\left(- \frac{432 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\tan^{2}{\left(3 x^{4} \right)}} + 864 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right) - \frac{72 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{36 x^{3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\sqrt{x + 3} \tan{\left(3 x^{4} \right)}} + \frac{108 x^{2} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{3 x \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right)}{2} - \frac{3 x \left(- \frac{576 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\tan^{2}{\left(3 x^{4} \right)}} + 1152 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right) + \frac{48 x^{3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\sqrt{x + 3} \tan{\left(3 x^{4} \right)}} + \frac{144 x^{2} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right)^{2} - \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\left(x + 3\right)^{\frac{3}{2}}}\right)}{4} + \frac{x \left(\frac{27648 x^{9} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{3}}{\tan^{3}{\left(3 x^{4} \right)}} - \frac{55296 x^{9} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\tan{\left(3 x^{4} \right)}} + 55296 x^{9} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right) \tan{\left(3 x^{4} \right)} - \frac{1728 x^{6} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\sqrt{x + 3} \tan^{2}{\left(3 x^{4} \right)}} + \frac{3456 x^{6} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\sqrt{x + 3}} - \frac{10368 x^{5} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\tan^{2}{\left(3 x^{4} \right)}} + 20736 x^{5} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right) - \frac{72 x^{3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\left(x + 3\right)^{\frac{3}{2}} \tan{\left(3 x^{4} \right)}} + \frac{432 x^{2} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\sqrt{x + 3} \tan{\left(3 x^{4} \right)}} + \frac{576 x \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right)^{3} + 3 \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right) \left(- \frac{576 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)^{2}}{\tan^{2}{\left(3 x^{4} \right)}} + 1152 x^{6} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right) + \frac{48 x^{3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\sqrt{x + 3} \tan{\left(3 x^{4} \right)}} + \frac{144 x^{2} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} - \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\left(x + 3\right)^{\frac{3}{2}}}\right) + \frac{3 \log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\left(x + 3\right)^{\frac{5}{2}}}\right)}{8} - x + \frac{3 \left(\frac{24 x^{3} \sqrt{x + 3} \left(\tan^{2}{\left(3 x^{4} \right)} + 1\right)}{\tan{\left(3 x^{4} \right)}} + \frac{\log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}}\right)^{2}}{4} + 3 - \frac{3 \log{\left(\tan{\left(3 x^{4} \right)} \right)}}{\sqrt{x + 3}} - \frac{3 \log{\left(\tan{\left(3 x^{4} \right)} \right)}}{4 \left(x + 3\right)^{\frac{3}{2}}}\right) e^{- x} \tan^{\sqrt{x + 3}}{\left(3 x^{4} \right)}$$

Simplificar

Gráfico

Derivada de x*(tan(3*(x^4)))^sqrt(x+3)exp(-x)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de x(tan(3(x^4)))^sqrt(x+3)exp(-x)

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de x*(tan(3*(x^4)))^sqrt(x+3)exp(-x)

Gráfico:

Definida a trozos:

Solución

Derivada de x(tan(3(x^4)))^sqrt(x+3)exp(-x)