Derivada de y=ecos^xsenx

Solución

Ha introducido [src]

     x          
E*cos (sin(x))*x

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

(E*cos(sin(x))^x)*x

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

$f{\left(x \right)} = e \cos^{x}{\left(\sin{\left(x \right)} \right)}$ ; 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. No logro encontrar los pasos en la búsqueda de esta derivada.
    
    Perola derivada
    
    $x^{x} \left(\log{\left(x \right)} + 1\right)$
  Entonces, como resultado: $e x^{x} \left(\log{\left(x \right)} + 1\right)$
$g{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
Como resultado de: $e x x^{x} \left(\log{\left(x \right)} + 1\right) + e \cos^{x}{\left(\sin{\left(x \right)} \right)}$
Simplificamos:

$e \left(x^{x + 1} \left(\log{\left(x \right)} + 1\right) + \cos^{x}{\left(\sin{\left(x \right)} \right)}\right)$

Respuesta:

$e \left(x^{x + 1} \left(\log{\left(x \right)} + 1\right) + \cos^{x}{\left(\sin{\left(x \right)} \right)}\right)$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

     x                  x         /  x*cos(x)*sin(sin(x))                   \
E*cos (sin(x)) + E*x*cos (sin(x))*|- -------------------- + log(cos(sin(x)))|
                                  \      cos(sin(x))                        /

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

               /                                            2     /                                            3                                                            /                                        2       2                               \        2       2                                                                                    3                         3       3                  2                      \                                               2       2                                 \
     x         |  /                    x*cos(x)*sin(sin(x))\      |  /                    x*cos(x)*sin(sin(x))\         2        /                    x*cos(x)*sin(sin(x))\ |     2      2*cos(x)*sin(sin(x))   x*cos (x)*sin (sin(x))   x*sin(x)*sin(sin(x))|   3*cos (x)*sin (sin(x))                       3*sin(x)*sin(sin(x))   x*cos(x)*sin(sin(x))   2*x*cos (x)*sin(sin(x))   2*x*cos (x)*sin (sin(x))   3*x*sin (sin(x))*cos(x)*sin(x)|          2      6*cos(x)*sin(sin(x))   3*x*cos (x)*sin (sin(x))   3*x*sin(x)*sin(sin(x))|
E*cos (sin(x))*|3*|-log(cos(sin(x))) + --------------------|  + x*|- |-log(cos(sin(x))) + --------------------|  - 3*cos (x) + 3*|-log(cos(sin(x))) + --------------------|*|x*cos (x) + -------------------- + ---------------------- - --------------------| - ---------------------- + 3*x*cos(x)*sin(x) + -------------------- + -------------------- - ----------------------- - ------------------------ + ------------------------------| - 3*x*cos (x) - -------------------- - ------------------------ + ----------------------|
               |  \                        cos(sin(x))     /      |  \                        cos(sin(x))     /                  \                        cos(sin(x))     / |                cos(sin(x))                2                    cos(sin(x))     |           2                                        cos(sin(x))            cos(sin(x))              cos(sin(x))                  3                             2                 |                     cos(sin(x))                 2                      cos(sin(x))      |
               \                                                  \                                                                                                         \                                        cos (sin(x))                            /        cos (sin(x))                                                                                                          cos (sin(x))                  cos (sin(x))         /                                              cos (sin(x))                               /

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

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de y=ecos^xsenx

Gráfico:

Definida a trozos:

Solución