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Derivada de:
Derivada de e^((3*x)^2)
Derivada de d/dx(x)
Derivada de (cos(x))^x^2
Derivada de (8*x-15)^5
Expresiones idénticas
x*sin(x)*tg(uno /x)*cos(x)/ctg(x)
x multiplicar por seno de (x) multiplicar por tg(1 dividir por x) multiplicar por coseno de (x) dividir por ctg(x)
x multiplicar por seno de (x) multiplicar por tg(uno dividir por x) multiplicar por coseno de (x) dividir por ctg(x)
xsin(x)tg(1/x)cos(x)/ctg(x)
xsinxtg1/xcosx/ctgx
x*sin(x)*tg(1 dividir por x)*cos(x) dividir por ctg(x)
Expresiones semejantes
x*sinx*tg(1/x)*cosx/ctg(x)

Derivada de la función/ x*sin(x)*tg(1/x)*cos(x)/ctg(x)

Derivada de xsin(x)tg(1/x)*cos(x)/ctg(x)

Solución

Ha introducido [src]

            /1\       
x*sin(x)*tan|-|*cos(x)
            \x/       
----------------------
        cot(x)

$$\frac{x \sin{\left(x \right)} \tan{\left(\frac{1}{x} \right)} \cos{\left(x \right)}}{\cot{\left(x \right)}}$$

(((x*sin(x))*tan(1/x))*cos(x))/cot(x)

Solución detallada

Se aplica la regla de la derivada parcial:

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

$f{\left(x \right)} = x \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}$ y $g{\left(x \right)} = \cot{\left(x \right)}$ .

Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
1. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$
  
  $\operatorname{f_{0}}{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$ :
  1. Según el principio, aplicamos: $x$ tenemos $1$
  $\operatorname{f_{1}}{\left(x \right)} = \cos{\left(x \right)}$ ; calculamos $\frac{d}{d x} \operatorname{f_{1}}{\left(x \right)}$ :
  1. La derivada del coseno es igual a menos el seno:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  $\operatorname{f_{2}}{\left(x \right)} = \sin{\left(x \right)}$ ; calculamos $\frac{d}{d x} \operatorname{f_{2}}{\left(x \right)}$ :
  1. La derivada del seno es igual al coseno:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  $\operatorname{f_{3}}{\left(x \right)} = \tan{\left(\frac{1}{x} \right)}$ ; calculamos $\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}$ :
  1. Reescribimos las funciones para diferenciar:
    
    $\tan{\left(\frac{1}{x} \right)} = \frac{\sin{\left(\frac{1}{x} \right)}}{\cos{\left(\frac{1}{x} \right)}}$
  2. Se aplica la regla de la derivada parcial:
    
    $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
    
    $f{\left(x \right)} = \sin{\left(\frac{1}{x} \right)}$ y $g{\left(x \right)} = \cos{\left(\frac{1}{x} \right)}$ .
    
    Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
    1. Sustituimos $u = \frac{1}{x}$ .
    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 $\frac{d}{d x} \frac{1}{x}$ :
      1. Según el principio, aplicamos: $\frac{1}{x}$ tenemos $- \frac{1}{x^{2}}$
      Como resultado de la secuencia de reglas:
      
      $- \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}$
    Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
    1. Sustituimos $u = \frac{1}{x}$ .
    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 $\frac{d}{d x} \frac{1}{x}$ :
      1. Según el principio, aplicamos: $\frac{1}{x}$ tenemos $- \frac{1}{x^{2}}$
      Como resultado de la secuencia de reglas:
      
      $\frac{\sin{\left(\frac{1}{x} \right)}}{x^{2}}$
    Ahora aplicamos la regla de la derivada de una divesión:
    
    $\frac{- \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}}}{\cos^{2}{\left(\frac{1}{x} \right)}}$
  Como resultado de: $\frac{x \left(- \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(\frac{1}{x} \right)}} - x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + x \cos^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}$
Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
1. Hay varias formas de calcular esta derivada.
  Method #1
  1. Reescribimos las funciones para diferenciar:
    
    $\cot{\left(x \right)} = \frac{1}{\tan{\left(x \right)}}$
  2. Sustituimos $u = \tan{\left(x \right)}$ .
  3. Según el principio, aplicamos: $\frac{1}{u}$ tenemos $- \frac{1}{u^{2}}$
  4. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \tan{\left(x \right)}$ :
    1. $\frac{d}{d x} \tan{\left(x \right)} = \frac{1}{\cos^{2}{\left(x \right)}}$
    Como resultado de la secuencia de reglas:
    
    $- \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan^{2}{\left(x \right)}}$
  Method #2
  1. Reescribimos las funciones para diferenciar:
    
    $\cot{\left(x \right)} = \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  2. Se aplica la regla de la derivada parcial:
    
    $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
    
    $f{\left(x \right)} = \cos{\left(x \right)}$ y $g{\left(x \right)} = \sin{\left(x \right)}$ .
    
    Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
    1. La derivada del coseno es igual a menos el seno:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
    1. La derivada del seno es igual al coseno:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    Ahora aplicamos la regla de la derivada de una divesión:
    
    $\frac{- \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}$
Ahora aplicamos la regla de la derivada de una divesión:

$\frac{\frac{x \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\cos{\left(x \right)} \tan^{2}{\left(x \right)}} + \left(\frac{x \left(- \frac{\sin^{2}{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{\cos^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(\frac{1}{x} \right)}} - x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + x \cos^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}\right) \cot{\left(x \right)}}{\cot^{2}{\left(x \right)}}$
Simplificamos:

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

  /                                                                                                                                           /           2/1\        2/1\        /1\\       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
  |                                                                                        /       /1\\                                       |    1 + tan |-|   2*tan |-|   6*tan|-||       |                                                                           /                                                                                      /       /1\\       \                                             //                                                                                      /       /1\\       \                                                                                               \                                                                                                                                                                                                        
  |                                                                                        |    tan|-||                         /       2/1\\ |            \x/         \x/        \x/|       |                                                                           |                                                                                      |    tan|-||       |                                             ||                                                                                      |    tan|-||       |                                                                                               |                                                                                                                                                                                                        
  |                                 /       2/1\\                            /       2/1\\ |       \x/|                       2*|1 + tan |-||*|3 + ----------- + --------- + --------|*sin(x)|            /                             /       2/1\\       \            |                                  /       2/1\\                         /       2/1\\ |       \x/|       |                                             ||                                  /       2/1\\                         /       2/1\\ |       \x/|       |            /                             /       2/1\\       \                                |                                      /  /                             /       2/1\\       \                          \                                                                                 
  |                               3*|1 + tan |-||*(-2*cos(x) + x*sin(x))   6*|1 + tan |-||*|1 + ------|*(x*cos(x) + sin(x))     \        \x// |          2            2         x    |       |            |                             |1 + tan |-||*sin(x)|            |                                2*|1 + tan |-||*(x*cos(x) + sin(x))   2*|1 + tan |-||*|1 + ------|*sin(x)|                                             ||                                2*|1 + tan |-||*(x*cos(x) + sin(x))   2*|1 + tan |-||*|1 + ------|*sin(x)|            |                             |1 + tan |-||*sin(x)|                                |                   /            2   \ |  |                             |1 + tan |-||*sin(x)|                          |                                                                                 
  |                         /1\     \        \x//                            \        \x// \      x   /                                       \         x            x               /       |            |                       /1\   \        \x//       |            |                          /1\     \        \x//                         \        \x// \      x   /       |               2       /1\     /       2   \ ||                          /1\     \        \x//                         \        \x// \      x   /       |            |                       /1\   \        \x//       |                             /1\|     /       2   \ |     1 + cot (x)| |  |                       /1\   \        \x//       |               2       /1\|                                                                                 
- |(3*sin(x) + x*cos(x))*tan|-| - -------------------------------------- - ------------------------------------------------ + ---------------------------------------------------------------|*cos(x) - 3*|(x*cos(x) + sin(x))*tan|-| - --------------------|*cos(x) + 3*|(-2*cos(x) + x*sin(x))*tan|-| + ----------------------------------- - -----------------------------------|*sin(x) + x*sin (x)*tan|-|   3*\1 + cot (x)/*||(-2*cos(x) + x*sin(x))*tan|-| + ----------------------------------- - -----------------------------------|*cos(x) + 2*|(x*cos(x) + sin(x))*tan|-| - --------------------|*sin(x) + x*cos(x)*sin(x)*tan|-||   6*\1 + cot (x)/*|-1 + -----------|*|- |(x*cos(x) + sin(x))*tan|-| - --------------------|*cos(x) + x*sin (x)*tan|-||       /                               2                  3\                     
  |                         \x/                      2                                             3                                                          3                              |            \                       \x/            x          /            |                          \x/                     2                                     2                |                       \x/                   ||                          \x/                     2                                     2                |            \                       \x/            x          /                             \x/|                   |          2     | \  \                       \x/            x          /                       \x//       |                  /       2   \      /       2   \ |                     
  \                                                 x                                             x                                                          x                               /                                                                           \                                                 x                                     x                 /                                             \\                                                 x                                     x                 /                                                                                               /                   \       cot (x)  /                                                                                         |         2      5*\1 + cot (x)/    3*\1 + cot (x)/ |                  /1\
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------- + 2*x*|2 + 2*cot (x) - ---------------- + ----------------|*cos(x)*sin(x)*tan|-|
                                                                                                                                                                                                    cot(x)                                                                                                                                                                                                                                                                                                                    2                                                                                                                                                                        cot(x)                                                              |                       2                  4        |                  \x/
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           cot (x)                                                                                                                                                                                                                                         \                    cot (x)            cot (x)     /

$$2 x \left(\frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{\cot^{4}{\left(x \right)}} - \frac{5 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 2 \cot^{2}{\left(x \right)} + 2\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \frac{6 \left(\frac{\cot^{2}{\left(x \right)} + 1}{\cot^{2}{\left(x \right)}} - 1\right) \left(x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \cos{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \left(x \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)} + 2 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \sin{\left(x \right)} + \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{2 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x^{2}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}}\right) \cos{\left(x \right)}\right)}{\cot^{2}{\left(x \right)}} + \frac{x \sin^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)} - 3 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x}\right) \cos{\left(x \right)} + 3 \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{2 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \sin{\left(x \right)}}{x^{2}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}}\right) \sin{\left(x \right)} - \left(\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \tan{\left(\frac{1}{x} \right)} - \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}} - \frac{6 \left(1 + \frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{3}} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \left(3 + \frac{6 \tan{\left(\frac{1}{x} \right)}}{x} + \frac{\tan^{2}{\left(\frac{1}{x} \right)} + 1}{x^{2}} + \frac{2 \tan^{2}{\left(\frac{1}{x} \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x^{3}}\right) \cos{\left(x \right)}}{\cot{\left(x \right)}}$$

Simplificar

Gráfico

Derivada de x*sin(x)*tg(1/x)*cos(x)/ctg(x)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de xsin(x)tg(1/x)*cos(x)/ctg(x)

Gráfico:

Definida a trozos:

Solución

Method #1

Method #2

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de x*sin(x)*tg(1/x)*cos(x)/ctg(x)

Gráfico:

Definida a trozos:

Solución

Method #1

Method #2

Derivada de xsin(x)tg(1/x)*cos(x)/ctg(x)