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Derivada de:
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Expresiones idénticas
x*sin(x)/x*sqrt(x^ dos +(sin(x)/x)^ dos)
x multiplicar por seno de (x) dividir por x multiplicar por raíz cuadrada de (x al cuadrado más ( seno de (x) dividir por x) al cuadrado )
x multiplicar por seno de (x) dividir por x multiplicar por raíz cuadrada de (x en el grado dos más ( seno de (x) dividir por x) en el grado dos)
x*sin(x)/x*√(x^2+(sin(x)/x)^2)
x*sin(x)/x*sqrt(x2+(sin(x)/x)2)
x*sinx/x*sqrtx2+sinx/x2
x*sin(x)/x*sqrt(x²+(sin(x)/x)²)
x*sin(x)/x*sqrt(x en el grado 2+(sin(x)/x) en el grado 2)
xsin(x)/xsqrt(x^2+(sin(x)/x)^2)
xsin(x)/xsqrt(x2+(sin(x)/x)2)
xsinx/xsqrtx2+sinx/x2
xsinx/xsqrtx^2+sinx/x^2
x*sin(x) dividir por x*sqrt(x^2+(sin(x) dividir por x)^2)
Expresiones semejantes
x*sin(x)/x*sqrt(x^2-(sin(x)/x)^2)
x*sinx/x*sqrt(x^2+(sinx/x)^2)

Derivada de la función/ x*sin(x)/x*sqrt(x^2+(sin(x)/x)^2)

Derivada de xsin(x)/xsqrt(x^2+(sin(x)/x)^2)

Solución

Ha introducido [src]

              ________________
             /              2 
x*sin(x)    /   2   /sin(x)\  
--------*  /   x  + |------|  
   x     \/         \  x   /

$$\frac{x \sin{\left(x \right)}}{x} \sqrt{x^{2} + \left(\frac{\sin{\left(x \right)}}{x}\right)^{2}}$$

((x*sin(x))/x)*sqrt(x^2 + (sin(x)/x)^2)

Solución detallada

Se aplica la regla de la derivada parcial:

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

$f{\left(x \right)} = x \sqrt{x^{2} + \left(\frac{\sin{\left(x \right)}}{x}\right)^{2}} \sin{\left(x \right)}$ y $g{\left(x \right)} = x$ .

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

$\frac{- x \sqrt{x^{2} + \left(\frac{\sin{\left(x \right)}}{x}\right)^{2}} \sin{\left(x \right)} + x \left(\frac{x \left(2 x + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right) \sin{\left(x \right)}}{x^{3}}\right) \sin{\left(x \right)}}{2 \sqrt{x^{2} + \left(\frac{\sin{\left(x \right)}}{x}\right)^{2}}} + x \sqrt{x^{2} + \left(\frac{\sin{\left(x \right)}}{x}\right)^{2}} \cos{\left(x \right)} + \sqrt{x^{2} + \left(\frac{\sin{\left(x \right)}}{x}\right)^{2}} \sin{\left(x \right)}\right)}{x^{2}}$
Simplificamos:

$\frac{\left(x^{5} \cos{\left(x \right)} + x^{4} \sin{\left(x \right)} + 2 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \sin^{3}{\left(x \right)}\right) \left|{x}\right|}{x^{3} \sqrt{x^{4} + \sin^{2}{\left(x \right)}}}$

Respuesta:

$\frac{\left(x^{5} \cos{\left(x \right)} + x^{4} \sin{\left(x \right)} + 2 x \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \sin^{3}{\left(x \right)}\right) \left|{x}\right|}{x^{3} \sqrt{x^{4} + \sin^{2}{\left(x \right)}}}$

Primera derivada [src]

                                                     /         2                           \       
                                                     |      sin (x) /  2*sin(x)   2*cos(x)\|       
                                                     |    x*-------*|- -------- + --------||       
                                                     |          2   |      2         x    ||       
     ________________                                |         x    \     x               /|       
    /              2                                 |x + ---------------------------------|*sin(x)
   /   2   /sin(x)\   /x*cos(x) + sin(x)   sin(x)\   \                 2*sin(x)            /       
  /   x  + |------|  *|----------------- - ------| + ----------------------------------------------
\/         \  x   /   \        x             x   /                    ________________             
                                                                     /              2              
                                                                    /   2   /sin(x)\               
                                                                   /   x  + |------|               
                                                                 \/         \  x   /

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

Simplificar

Segunda derivada [src]

                                                                                   /                                     2                                                                                                                             \                                                   
                                                                                   |     /    /  sin(x)         \       \                                                                                                                              |                                                   
                                                                                   |     |    |- ------ + cos(x)|*sin(x)|                                                                                                                              |                                                   
                                                                                   |     |    \    x            /       |                         2                                /  2*sin(x)   2*cos(x)         \                                    |                                                   
                                                                                   |     |x + --------------------------|      /  sin(x)         \    /  sin(x)         \          |- -------- + -------- + sin(x)|*sin(x)   /  sin(x)         \       |                                                   
                                                                                   |     |                 2            |    2*|- ------ + cos(x)|    |- ------ + cos(x)|*cos(x)   |      2         x             |          |- ------ + cos(x)|*sin(x)|                                                   
                                                                                   |     \                x             /      \    x            /    \    x            /          \     x                        /          \    x            /       |                                                   
        ______________                                                             |-1 + --------------------------------- - ---------------------- + -------------------------- + --------------------------------------- - --------------------------|*sin(x)     /    /  sin(x)         \       \       
       /         2                                                                 |                        2                           2                          2                                   2                                  3            |            |    |- ------ + cos(x)|*sin(x)|       
      /   2   sin (x)  /                       2*sin(x)   2*(x*cos(x) + sin(x))\   |                 2   sin (x)                       x                          x                                   x                                  x             |            |    \    x            /       |       
     /   x  + ------- *|-2*cos(x) + x*sin(x) - -------- + ---------------------|   |                x  + -------                                                                                                                                       |          2*|x + --------------------------|*cos(x)
    /             2    \                          x                 x          /   |                         2                                                                                                                                         |            |                 2            |       
  \/             x                                                                 \                        x                                                                                                                                          /            \                x             /       
- ------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------
                                        x                                                                                                                            ______________                                                                                                ______________          
                                                                                                                                                                    /         2                                                                                                   /         2              
                                                                                                                                                                   /   2   sin (x)                                                                                               /   2   sin (x)           
                                                                                                                                                                  /   x  + -------                                                                                              /   x  + -------           
                                                                                                                                                                 /             2                                                                                               /             2             
                                                                                                                                                               \/             x                                                                                              \/             x

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

Simplificar

Tercera derivada [src]

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

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

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Expresiones idénticas

Expresiones semejantes

Derivada de xsin(x)/xsqrt(x^2+(sin(x)/x)^2)

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de x*sin(x)/x*sqrt(x^2+(sin(x)/x)^2)

Gráfico:

Definida a trozos:

Solución

Derivada de xsin(x)/xsqrt(x^2+(sin(x)/x)^2)