Derivada de x*exp(-x)ln(ln(x)/sin(1/(x^2-6x)))

Ha introducido [src]

   -x    /    log(x)   \
x*e  *log|-------------|
         |   /   1    \|
         |sin|--------||
         |   | 2      ||
         \   \x  - 6*x//

x e^{- x} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x^{2} - 6 x} \right)}} \right)}

(x*exp(-x))*log(log(x)/sin(1/(x^2 - 6*x)))

Solución detallada

Se aplica la regla de la derivada parcial:

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

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

$\left(- x e^{x} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x^{2} - 6 x} \right)}} \right)} + \left(\frac{x \left(\frac{\left(2 x - 6\right) \log{\left(x \right)} \cos{\left(\frac{1}{x^{2} - 6 x} \right)}}{\left(x^{2} - 6 x\right)^{2}} + \frac{\sin{\left(\frac{1}{x^{2} - 6 x} \right)}}{x}\right)}{\log{\left(x \right)} \sin{\left(\frac{1}{x^{2} - 6 x} \right)}} + \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x^{2} - 6 x} \right)}} \right)}\right) e^{x}\right) e^{- 2 x}$
Simplificamos:

$\frac{\left(- x^{4} \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + 13 x^{3} \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + x^{3} - 48 x^{2} \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} - 12 x^{2} + 36 x \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + \frac{2 x \log{\left(x \right)}}{\tan{\left(\frac{1}{x \left(x - 6\right)} \right)}} + 36 x - \frac{6 \log{\left(x \right)}}{\tan{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) e^{- x}}{x \left(x - 6\right)^{2} \log{\left(x \right)}}$

Respuesta:

$\frac{\left(- x^{4} \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + 13 x^{3} \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + x^{3} - 48 x^{2} \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} - 12 x^{2} + 36 x \log{\left(x \right)} \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + \frac{2 x \log{\left(x \right)}}{\tan{\left(\frac{1}{x \left(x - 6\right)} \right)}} + 36 x - \frac{6 \log{\left(x \right)}}{\tan{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) e^{- x}}{x \left(x - 6\right)^{2} \log{\left(x \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                                       /                               /   1    \       \                  
                                       |                  (6 - 2*x)*cos|--------|*log(x)|                  
                                       |                               | 2      |       |                  
                                       |       1                       \x  - 6*x/       |  -x    /   1    \
                                     x*|--------------- - ------------------------------|*e  *sin|--------|
                                       |     /   1    \               2                 |        | 2      |
                                       |x*sin|--------|     / 2      \     2/   1    \  |        \x  - 6*x/
                                       |     | 2      |     \x  - 6*x/ *sin |--------|  |                  
                                       |     \x  - 6*x/                     | 2      |  |                  
/     -x    -x\    /    log(x)   \     \                                    \x  - 6*x/  /                  
\- x*e   + e  /*log|-------------| + ----------------------------------------------------------------------
                   |   /   1    \|                                   log(x)                                
                   |sin|--------||                                                                         
                   |   | 2      ||                                                                         
                   \   \x  - 6*x//

\frac{x \left(- \frac{\left(6 - 2 x\right) \log{\left(x \right)} \cos{\left(\frac{1}{x^{2} - 6 x} \right)}}{\left(x^{2} - 6 x\right)^{2} \sin^{2}{\left(\frac{1}{x^{2} - 6 x} \right)}} + \frac{1}{x \sin{\left(\frac{1}{x^{2} - 6 x} \right)}}\right) e^{- x} \sin{\left(\frac{1}{x^{2} - 6 x} \right)}}{\log{\left(x \right)}} + \left(- x e^{- x} + e^{- x}\right) \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x^{2} - 6 x} \right)}} \right)}

Simplificar

Segunda derivada [src]

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

\left(\left(x - 2\right) \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} - \frac{2 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 1\right)}{x \log{\left(x \right)}} - \frac{\frac{1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}}{\log{\left(x \right)}} + 1 - \frac{2 \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{2 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{4 \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{4 \left(x - 3\right)^{2} \log{\left(x \right)}}{x^{2} \left(x - 6\right)^{4}} - \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{2} \left(x - 6\right)^{4} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}}{x \log{\left(x \right)}}\right) e^{- x}

Simplificar

Tercera derivada [src]

/                                                        /    1     \            /           /    1     \                                              /    1     \             2    /    1     \                    2    2/    1     \       \     /                  /    1     \       \                                                                                /                  /    1     \       \     /                  /    1     \       \                                                                                                                                                                                                                            /           /    1     \                                              /    1     \             2    /    1     \                    2    2/    1     \       \                               /                  /    1     \       \                                                                                                                                                                              /                  /    1     \       \                                                                                            /                      /    1     \                                                                                                                                 /                  /    1     \       \                                                              \\    
|                                          2*(-3 + x)*cos|----------|*log(x)     |      2*cos|----------|*log(x)             2           4*(-3 + x)*cos|----------|   8*(-3 + x) *cos|----------|*log(x)   8*(-3 + x) *cos |----------|*log(x)|     |    2*(-3 + x)*cos|----------|*log(x)|                                                                                |    2*(-3 + x)*cos|----------|*log(x)|     |    2*(-3 + x)*cos|----------|*log(x)|                                                                                                                                                                                                                            |      2*cos|----------|*log(x)             2           4*(-3 + x)*cos|----------|   8*(-3 + x) *cos|----------|*log(x)   8*(-3 + x) *cos |----------|*log(x)|                               |    2*(-3 + x)*cos|----------|*log(x)|                                                                                                                                                                              |    2*(-3 + x)*cos|----------|*log(x)|                                                                                            |        2*(-3 + x)*cos|----------|*log(x)                                                                                                                          |    2*(-3 + x)*cos|----------|*log(x)|                                                              ||    
|                                                        \x*(-6 + x)/            |           \x*(-6 + x)/          4*(-3 + x) *log(x)                  \x*(-6 + x)/                  \x*(-6 + x)/                          \x*(-6 + x)/       |     |                  \x*(-6 + x)/       |                                                                              2 |                  \x*(-6 + x)/       |     |                  \x*(-6 + x)/       |    /    1     \                                                                                                                                                                                                            |           \x*(-6 + x)/          4*(-3 + x) *log(x)                  \x*(-6 + x)/                  \x*(-6 + x)/                          \x*(-6 + x)/       |    /    1     \             2 |                  \x*(-6 + x)/       |    /    1     \                                                                                                                                                              |                  \x*(-6 + x)/       |             /    1     \                                                                   |                      \x*(-6 + x)/                                                                                                                                 |                  \x*(-6 + x)/       |             /    1     \                                     ||    
|                                      1 + ---------------------------------   2*|-1 + ------------------------- + ------------------ + --------------------------- - ---------------------------------- + -----------------------------------|   2*|1 + ---------------------------------|                                                                    4*(-3 + x) *|1 + ---------------------------------|   2*|1 + ---------------------------------|*cos|----------|                                                                                                                                                                                                 4*(-3 + x)*|-1 + ------------------------- + ------------------ + --------------------------- - ---------------------------------- + -----------------------------------|*cos|----------|   8*(-3 + x) *|1 + ---------------------------------|*cos|----------|                                                                                                                                                            4*|1 + ---------------------------------|*(-3 + x)*cos|----------|                                                                   |    1 + ---------------------------------                                                                                                                        2*|1 + ---------------------------------|*(-3 + x)*cos|----------|                                     ||    
|                                                       2    /    1     \        |             2    /    1     \       2         4                2    /    1     \                3    /    1     \           2         4    2/    1     \   |     |                 2    /    1     \   |            /    1     \                                                        |                 2    /    1     \   |     |                 2    /    1     \   |    \x*(-6 + x)/                                   2    /    1     \                  /    1     \                         /    1     \              2    2/    1     \              3    2/    1     \                     |             2    /    1     \       2         4                2    /    1     \                3    /    1     \           2         4    2/    1     \   |    \x*(-6 + x)/               |                 2    /    1     \   |    \x*(-6 + x)/         2/    1     \                              3    /    1     \                     3    /    1     \                     3    3/    1     \            |                 2    /    1     \   |             \x*(-6 + x)/     /                  /    1     \       \                       |                     2    /    1     \                                 /    1     \                         /    1     \             2    2/    1     \            |                 2    /    1     \   |             \x*(-6 + x)/             2    /    1     \       ||    
|                                             x*(-6 + x) *sin|----------|        |     (-6 + x) *sin|----------|      x *(-6 + x)       x*(-6 + x) *sin|----------|      x*(-6 + x) *sin|----------|          x *(-6 + x) *sin |----------|   |     |       x*(-6 + x) *sin|----------|   |       6*cos|----------|                  2              3                      |       x*(-6 + x) *sin|----------|   |     |       x*(-6 + x) *sin|----------|   |                                        24*(-3 + x) *cos|----------|   24*(-3 + x)*cos|----------|*log(x)    6*(-3 + x)*cos|----------|   24*(-3 + x) *cos |----------|   96*(-3 + x) *cos |----------|*log(x)              |     (-6 + x) *sin|----------|      x *(-6 + x)       x*(-6 + x) *sin|----------|      x*(-6 + x) *sin|----------|          x *(-6 + x) *sin |----------|   |                               |       x*(-6 + x) *sin|----------|   |                   24*cos |----------|*(-3 + x)*log(x)   40*(-3 + x) *cos|----------|*log(x)   48*(-3 + x) *cos|----------|*log(x)   48*(-3 + x) *cos |----------|*log(x)     |       x*(-6 + x) *sin|----------|   |                              |    2*(-3 + x)*cos|----------|*log(x)|                       |           x*(-6 + x) *sin|----------|                2           2*cos|----------|*log(x)    4*(-3 + x)*cos|----------|   8*(-3 + x) *cos |----------|*log(x)     |       x*(-6 + x) *sin|----------|   |                            8*(-3 + x) *cos|----------|*log(x)||    
|                                                            \x*(-6 + x)/        \                  \x*(-6 + x)/                                       \x*(-6 + x)/                     \x*(-6 + x)/                           \x*(-6 + x)/   /     \                      \x*(-6 + x)/   /            \x*(-6 + x)/       12*(-3 + x)    48*(-3 + x) *log(x)               \                      \x*(-6 + x)/   /     \                      \x*(-6 + x)/   /                   12*(-3 + x)*log(x)                   \x*(-6 + x)/                  \x*(-6 + x)/                         \x*(-6 + x)/                    \x*(-6 + x)/                    \x*(-6 + x)/                     \                  \x*(-6 + x)/                                       \x*(-6 + x)/                     \x*(-6 + x)/                           \x*(-6 + x)/   /                               \                      \x*(-6 + x)/   /                          \x*(-6 + x)/                                   \x*(-6 + x)/                          \x*(-6 + x)/                           \x*(-6 + x)/            \                      \x*(-6 + x)/   /                              |                  \x*(-6 + x)/       |                       |                          \x*(-6 + x)/      4*(-3 + x) *log(x)         \x*(-6 + x)/                         \x*(-6 + x)/                   \x*(-6 + x)/            \                      \x*(-6 + x)/   /                                           \x*(-6 + x)/       ||    
|                                  2 + ------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------- + ------------------------- + ------------ - ------------------- - --------------------------------------------------- - --------------------------------------------------------- + ------------------ - ---------------------------- - ---------------------------------- - --------------------------- + ----------------------------- - ------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------- + ----------------------------------- + ----------------------------------- + ----------------------------------- + ------------------------------------ + ------------------------------------------------------------------   3*|1 + ---------------------------------|*(-2 + x)   3*(-1 + x)*|1 + ------------------------------------- - ------------------ - ------------------------- - --------------------------- - ----------------------------------- + ------------------------------------------------------------------ + ----------------------------------||    
|                                                      log(x)                                                                                               log(x)                                                                                                    2                               2    /    1     \    2         4        2         5                           2         4                                              2    /    1     \                                4                 3    /    1     \                3    /    1     \                  2    /    1     \    2         4    2/    1     \       2         5    2/    1     \                                                                                                2    /    1     \                                                                                                                3    /    1     \                                     4    2/    1     \           3         6    /    1     \                    4    /    1     \           3         6    3/    1     \                                 2           /    1     \                     |                 2    /    1     \   |                       |                    log(x)                      2         4              2    /    1     \             2    /    1     \       2         4    2/    1     \                                   2    /    1     \                                    3    /    1     \    ||    
|                                                                                                                                                                                                                                                                  log (x)                    (-6 + x) *sin|----------|   x *(-6 + x)        x *(-6 + x)                           x *(-6 + x)                                       (-6 + x) *sin|----------|                      x*(-6 + x)        x*(-6 + x) *sin|----------|        (-6 + x) *sin|----------|        x*(-6 + x) *sin|----------|   x *(-6 + x) *sin |----------|      x *(-6 + x) *sin |----------|                                                                                      x*(-6 + x) *sin|----------|                                                                                                      x*(-6 + x) *sin|----------|                           x*(-6 + x) *sin |----------|          x *(-6 + x) *sin|----------|          x*(-6 + x) *sin|----------|          x *(-6 + x) *sin |----------|                       x*(-6 + x) *log(x)*sin|----------|                     |       x*(-6 + x) *sin|----------|   |                       |                                               x *(-6 + x)       (-6 + x) *sin|----------|   x*(-6 + x) *sin|----------|      x *(-6 + x) *sin |----------|                         x*(-6 + x) *sin|----------|                          x*(-6 + x) *sin|----------|    ||    
|              /     log(x)    \                                                                                                                                                                                                                                                                           \x*(-6 + x)/                                                                                                                           \x*(-6 + x)/                                                       \x*(-6 + x)/                     \x*(-6 + x)/                       \x*(-6 + x)/                    \x*(-6 + x)/                       \x*(-6 + x)/                                                                                                     \x*(-6 + x)/                                                                                                                     \x*(-6 + x)/                                           \x*(-6 + x)/                          \x*(-6 + x)/                         \x*(-6 + x)/                           \x*(-6 + x)/                                             \x*(-6 + x)/                     \                      \x*(-6 + x)/   /                       \                                                                              \x*(-6 + x)/                  \x*(-6 + x)/                       \x*(-6 + x)/                                        \x*(-6 + x)/                                         \x*(-6 + x)/    /|  -x
|- (-3 + x)*log|---------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*e  
|              |   /    1     \|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               x*log(x)                                                                                                                                                               2                                                                                                                                             |    
|              |sin|----------||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   x *log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              x *log(x)                                                                                                                                      |    
\              \   \x*(-6 + x)//                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         /

\left(- \left(x - 3\right) \log{\left(\frac{\log{\left(x \right)}}{\sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} \right)} + \frac{3 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 2\right)}{x \log{\left(x \right)}} + \frac{3 \left(x - 1\right) \left(\frac{1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}}{\log{\left(x \right)}} + 1 - \frac{2 \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{2 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{4 \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{4 \left(x - 3\right)^{2} \log{\left(x \right)}}{x^{2} \left(x - 6\right)^{4}} - \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{2} \left(x - 6\right)^{4} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right)}{x^{2} \log{\left(x \right)}} + \frac{\frac{1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}}{\log{\left(x \right)}} + \frac{2 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right)}{\log{\left(x \right)}^{2}} - \frac{2 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{2 \left(-1 + \frac{2 \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{4 \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{4 \left(x - 3\right)^{2} \log{\left(x \right)}}{x^{2} \left(x - 6\right)^{4}} + \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{2} \left(x - 6\right)^{4} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right)}{\log{\left(x \right)}} + 2 + \frac{6 \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{24 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{4 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \log{\left(x \right)} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{8 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 3\right)^{2} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{4 \left(x - 3\right) \left(-1 + \frac{2 \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{\left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{4 \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{4 \left(x - 3\right)^{2} \log{\left(x \right)}}{x^{2} \left(x - 6\right)^{4}} + \frac{8 \left(x - 3\right)^{2} \log{\left(x \right)} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{2} \left(x - 6\right)^{4} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{6 \left(x - 3\right) \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{24 \left(x - 3\right)^{2} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{3} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{48 \left(x - 3\right)^{3} \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{4} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{12 \left(x - 3\right) \log{\left(x \right)}}{x \left(x - 6\right)^{4}} + \frac{24 \left(x - 3\right) \log{\left(x \right)} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{4} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{4 \left(1 + \frac{2 \left(x - 3\right) \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x \left(x - 6\right)^{2} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}}\right) \left(x - 3\right)^{2}}{x^{2} \left(x - 6\right)^{4}} + \frac{12 \left(x - 3\right)^{2}}{x^{2} \left(x - 6\right)^{4}} + \frac{24 \left(x - 3\right)^{2} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{2} \left(x - 6\right)^{4} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}} - \frac{48 \left(x - 3\right)^{3} \log{\left(x \right)}}{x^{2} \left(x - 6\right)^{5}} - \frac{96 \left(x - 3\right)^{3} \log{\left(x \right)} \cos^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{2} \left(x - 6\right)^{5} \sin^{2}{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{40 \left(x - 3\right)^{3} \log{\left(x \right)} \cos{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{3} \left(x - 6\right)^{6} \sin{\left(\frac{1}{x \left(x - 6\right)} \right)}} + \frac{48 \left(x - 3\right)^{3} \log{\left(x \right)} \cos^{3}{\left(\frac{1}{x \left(x - 6\right)} \right)}}{x^{3} \left(x - 6\right)^{6} \sin^{3}{\left(\frac{1}{x \left(x - 6\right)} \right)}}}{x^{2} \log{\left(x \right)}}\right) e^{- x}

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Gráfico

Derivada de x*exp(-x)ln(ln(x)/sin(1/(x^2-6x)))

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Derivada de x*exp(-x)ln(ln(x)/sin(1/(x^2-6x)))

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