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Derivada de la función/ x*excos(x)*sin((x)^(1/2))*e^(sin(x))p(-x)

Derivada de xexcos(x)sin((x)^(1/2))*e^(sin(x))p(-x)

Solución

Ha introducido [src]

   x           /  ___\  sin(x)       
x*E *cos(x)*sin\\/ x /*E      *p*(-x)

$$- x p e^{\sin{\left(x \right)}} e^{x} x \cos{\left(x \right)} \sin{\left(\sqrt{x} \right)}$$

(((((x*E^x)*cos(x))*sin(sqrt(x)))*E^sin(x))*p)*(-x)

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

$f{\left(x \right)} = p e^{\sin{\left(x \right)}} e^{x} x \cos{\left(x \right)} \sin{\left(\sqrt{x} \right)}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \operatorname{f_{4}}{\left(x \right)} = \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{4}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{4}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{3}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \operatorname{f_{4}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{2}}{\left(x \right)} + \operatorname{f_{0}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \operatorname{f_{4}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{1}}{\left(x \right)} + \operatorname{f_{1}}{\left(x \right)} \operatorname{f_{2}}{\left(x \right)} \operatorname{f_{3}}{\left(x \right)} \operatorname{f_{4}}{\left(x \right)} \frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$
    
    $\operatorname{f_{0}}{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} \operatorname{f_{0}}{\left(x \right)}$ :
    1. Según el principio, aplicamos: $x$ tenemos $1$
    $\operatorname{f_{1}}{\left(x \right)} = e^{x}$ ; calculamos $\frac{d}{d x} \operatorname{f_{1}}{\left(x \right)}$ :
    1. Derivado $e^{x}$ es.
    $\operatorname{f_{2}}{\left(x \right)} = e^{\sin{\left(x \right)}}$ ; calculamos $\frac{d}{d x} \operatorname{f_{2}}{\left(x \right)}$ :
    1. Sustituimos $u = \sin{\left(x \right)}$ .
    2. Derivado $e^{u}$ es.
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \sin{\left(x \right)}$ :
      1. La derivada del seno es igual al coseno:
        
        $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
      Como resultado de la secuencia de reglas:
      
      $e^{\sin{\left(x \right)}} \cos{\left(x \right)}$
    $\operatorname{f_{3}}{\left(x \right)} = \cos{\left(x \right)}$ ; calculamos $\frac{d}{d x} \operatorname{f_{3}}{\left(x \right)}$ :
    1. La derivada del coseno es igual a menos el seno:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    $\operatorname{f_{4}}{\left(x \right)} = \sin{\left(\sqrt{x} \right)}$ ; calculamos $\frac{d}{d x} \operatorname{f_{4}}{\left(x \right)}$ :
    1. Sustituimos $u = \sqrt{x}$ .
    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 $\frac{d}{d x} \sqrt{x}$ :
      1. Según el principio, aplicamos: $\sqrt{x}$ tenemos $\frac{1}{2 \sqrt{x}}$
      Como resultado de la secuencia de reglas:
      
      $\frac{\cos{\left(\sqrt{x} \right)}}{2 \sqrt{x}}$
    Como resultado de: $\frac{\sqrt{x} e^{x} e^{\sin{\left(x \right)}} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)}}{2} - x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \sin{\left(x \right)} + x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} + x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)} + e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)}$
  Entonces, como resultado: $p \left(\frac{\sqrt{x} e^{x} e^{\sin{\left(x \right)}} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)}}{2} - x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \sin{\left(x \right)} + x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} + x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)} + e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)}\right)$
$g{\left(x \right)} = - x$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
  1. Según el principio, aplicamos: $x$ tenemos $1$
  Entonces, como resultado: $-1$
Como resultado de: $- p x \left(\frac{\sqrt{x} e^{x} e^{\sin{\left(x \right)}} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)}}{2} - x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \sin{\left(x \right)} + x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} + x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)} + e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)}\right) - p x e^{x} e^{\sin{\left(x \right)}} \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)}$
Simplificamos:

$- \frac{p x \left(\sqrt{x} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)} + 2 x \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} + 2 \sqrt{2} x \sin{\left(\sqrt{x} \right)} \cos{\left(x + \frac{\pi}{4} \right)} + 4 \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)}\right) e^{x + \sin{\left(x \right)}}}{2}$

Respuesta:

$- \frac{p x \left(\sqrt{x} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)} + 2 x \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} + 2 \sqrt{2} x \sin{\left(\sqrt{x} \right)} \cos{\left(x + \frac{\pi}{4} \right)} + 4 \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)}\right) e^{x + \sin{\left(x \right)}}}{2}$

Primera derivada [src]

      //                                                  ___           /  ___\  x\                                          \                                   
      ||// x      x\             x       \    /  ___\   \/ x *cos(x)*cos\\/ x /*e |  sin(x)        2     x  sin(x)    /  ___\|               x  sin(x)    /  ___\
- p*x*||\\E  + x*e /*cos(x) - x*e *sin(x)/*sin\\/ x / + --------------------------|*e       + x*cos (x)*e *e      *sin\\/ x /| - p*x*cos(x)*e *e      *sin\\/ x /
      \\                                                            2             /                                          /

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

Simplificar

Segunda derivada [src]

  /                                             /                                                                                                                                                    /   /  ___\      /  ___\\                                           /  ___\                                             \                                                   \           
  |                                             |    /                                   /  ___\     ___           /  ___\\                                                              /  ___\     |sin\\/ x /   cos\\/ x /|          4*(x*sin(x) - (1 + x)*cos(x))*cos\\/ x /       /     2            \           /  ___\|                                                   |           
  |                                           x*|- 4*\- 2*(x*sin(x) - (1 + x)*cos(x))*sin\\/ x / + \/ x *cos(x)*cos\\/ x //*cos(x) + 4*(x*cos(x) - (2 + x)*cos(x) + 2*(1 + x)*sin(x))*sin\\/ x / + x*|---------- + ----------|*cos(x) + ---------------------------------------- + 4*x*\- cos (x) + sin(x)/*cos(x)*sin\\/ x /|                                                   |           
  |                                             |                                                                                                                                                    |    x            3/2   |                             ___                                                               |                                                   |           
  |                                 /  ___\     \                                                                                                                                                    \                x      /                           \/ x                                                                /     ___           /  ___\          2       /  ___\|  x  sin(x)
p*|2*(x*sin(x) - (1 + x)*cos(x))*sin\\/ x / + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - \/ x *cos(x)*cos\\/ x / - 2*x*cos (x)*sin\\/ x /|*e *e      
  \                                                                                                                                                                                  4                                                                                                                                                                                           /

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

Simplificar

Tercera derivada [src]

  /                                                                                                                                                    /                                                                                                                 /   /  ___\      /  ___\\     /                                                                /   /  ___\      /  ___\\                                           /  ___\\                                                                                                             /     /  ___\        /  ___\        /  ___\\                                                               /  ___\                                                  \                                                  /   /  ___\      /  ___\\                                                    \           
  |                                                                                                                                                    |                                                                         /  ___\                                 |sin\\/ x /   cos\\/ x /|     |                                                    /  ___\     |sin\\/ x /   cos\\/ x /|          4*(x*sin(x) - (1 + x)*cos(x))*cos\\/ x /|             /     2            \ /                                   /  ___\     ___           /  ___\\     |  cos\\/ x /   3*sin\\/ x /   3*cos\\/ x /|          12*(x*cos(x) - (2 + x)*cos(x) + 2*(1 + x)*sin(x))*cos\\/ x /          2    /       2              \    /  ___\|                                                  |sin\\/ x /   cos\\/ x /|                                                    |           
  |                                                                                                                                                  x*|- 8*(x*sin(x) + (3 + x)*cos(x) - 3*(1 + x)*cos(x) - 3*(2 + x)*sin(x))*sin\\/ x / - 6*(x*sin(x) - (1 + x)*cos(x))*|---------- + ----------| + 6*|4*(x*cos(x) - (2 + x)*cos(x) + 2*(1 + x)*sin(x))*sin\\/ x / + x*|---------- + ----------|*cos(x) + ----------------------------------------|*cos(x) + 12*\- cos (x) + sin(x)/*\- 2*(x*sin(x) - (1 + x)*cos(x))*sin\\/ x / + \/ x *cos(x)*cos\\/ x // - x*|- ---------- + ------------ + ------------|*cos(x) + ------------------------------------------------------------ + 8*x*cos (x)*\1 - cos (x) + 3*sin(x)/*sin\\/ x /|                                              3*x*|---------- + ----------|*cos(x)                                             |           
  |                                                                                                                                                    |                                                                                                                 |    x            3/2   |     |                                                                |    x            3/2   |                             ___                  |                                                                                                             |      3/2            2             5/2    |                                       ___                                                                              |                                    /  ___\       |    x            3/2   |                                                    |           
  |    /                                   /  ___\     ___           /  ___\\                                                              /  ___\     \                                                                                                                 \                x      /     \                                                                \                x      /                           \/ x                   /                                                                                                             \     x              x             x       /                                     \/ x                                                                               /   3*(x*sin(x) - (1 + x)*cos(x))*cos\\/ x /       \                x      /              /     2            \           /  ___\|  x  sin(x)
p*|- 3*\- 2*(x*sin(x) - (1 + x)*cos(x))*sin\\/ x / + \/ x *cos(x)*cos\\/ x //*cos(x) + 3*(x*cos(x) - (2 + x)*cos(x) + 2*(1 + x)*sin(x))*sin\\/ x / + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------- + ------------------------------------ + 3*x*\- cos (x) + sin(x)/*cos(x)*sin\\/ x /|*e *e      
  |                                                                                                                                                                                                                                                                                                                                                                                                                                          8                                                                                                                                                                                                                                                                                                              ___                                      4                                                               |           
  \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \/ x                                                                                                       /

$$p \left(\frac{3 x \left(\frac{\sin{\left(\sqrt{x} \right)}}{x} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \cos{\left(x \right)}}{4} + 3 x \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \sin{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{x \left(- x \left(\frac{3 \sin{\left(\sqrt{x} \right)}}{x^{2}} - \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3 \cos{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}}}\right) \cos{\left(x \right)} + 8 x \left(3 \sin{\left(x \right)} - \cos^{2}{\left(x \right)} + 1\right) \sin{\left(\sqrt{x} \right)} \cos^{2}{\left(x \right)} - 6 \left(\frac{\sin{\left(\sqrt{x} \right)}}{x} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \left(x \sin{\left(x \right)} - \left(x + 1\right) \cos{\left(x \right)}\right) + 12 \left(\sqrt{x} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)} - 2 \left(x \sin{\left(x \right)} - \left(x + 1\right) \cos{\left(x \right)}\right) \sin{\left(\sqrt{x} \right)}\right) \left(\sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) + 6 \left(x \left(\frac{\sin{\left(\sqrt{x} \right)}}{x} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \cos{\left(x \right)} + 4 \left(x \cos{\left(x \right)} + 2 \left(x + 1\right) \sin{\left(x \right)} - \left(x + 2\right) \cos{\left(x \right)}\right) \sin{\left(\sqrt{x} \right)} + \frac{4 \left(x \sin{\left(x \right)} - \left(x + 1\right) \cos{\left(x \right)}\right) \cos{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) \cos{\left(x \right)} - 8 \left(x \sin{\left(x \right)} - 3 \left(x + 1\right) \cos{\left(x \right)} - 3 \left(x + 2\right) \sin{\left(x \right)} + \left(x + 3\right) \cos{\left(x \right)}\right) \sin{\left(\sqrt{x} \right)} + \frac{12 \left(x \cos{\left(x \right)} + 2 \left(x + 1\right) \sin{\left(x \right)} - \left(x + 2\right) \cos{\left(x \right)}\right) \cos{\left(\sqrt{x} \right)}}{\sqrt{x}}\right)}{8} - 3 \left(\sqrt{x} \cos{\left(\sqrt{x} \right)} \cos{\left(x \right)} - 2 \left(x \sin{\left(x \right)} - \left(x + 1\right) \cos{\left(x \right)}\right) \sin{\left(\sqrt{x} \right)}\right) \cos{\left(x \right)} + 3 \left(x \cos{\left(x \right)} + 2 \left(x + 1\right) \sin{\left(x \right)} - \left(x + 2\right) \cos{\left(x \right)}\right) \sin{\left(\sqrt{x} \right)} + \frac{3 \left(x \sin{\left(x \right)} - \left(x + 1\right) \cos{\left(x \right)}\right) \cos{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) e^{x} e^{\sin{\left(x \right)}}$$

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de xexcos(x)sin((x)^(1/2))*e^(sin(x))p(-x)

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de x*excos(x)*sin((x)^(1/2))*e^(sin(x))p(-x)

Gráfico:

Definida a trozos:

Solución

Derivada de xexcos(x)sin((x)^(1/2))*e^(sin(x))p(-x)