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Derivada de:
Derivada de x^-8
Derivada de x^2/lnx
Derivada de √x+2
Derivada de (t^(2)+1)÷(t^(1÷2)-1)
Expresiones idénticas
x*sin(x)^(sin(x*sin(x)))
x multiplicar por seno de (x) en el grado ( seno de (x multiplicar por seno de (x)))
x*sin(x)(sin(x*sin(x)))
x*sinxsinx*sinx
xsin(x)^(sin(xsin(x)))
xsin(x)(sin(xsin(x)))
xsinxsinxsinx
xsinx^sinxsinx
Expresiones semejantes
x*sinx^(sin(x*sinx))
Expresiones con funciones
Seno sin
sin(x+2)
sin(x)^sin(x)
sin(x)/(1-x)
sin(x^4)
sin(x)/(1+tan(x))
Seno sin
sin(x+2)
sin(x)^sin(x)
sin(x)/(1-x)
sin(x^4)
sin(x)/(1+tan(x))
Seno sin
sin(x+2)
sin(x)^sin(x)
sin(x)/(1-x)
sin(x^4)
sin(x)/(1+tan(x))

Derivada de la función/ x*sin/ sin(x)/ x*sin(x)^(sin(x*sin(x)))

Derivada de xsin(x)^(sin(xsin(x)))

Solución

Ha introducido [src]

     sin(x*sin(x))   
x*sin             (x)

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

x*sin(x)^sin(x*sin(x))

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

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

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

Otras calculadoras

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de xsin(x)^(sin(xsin(x)))

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de x*sin(x)^(sin(x*sin(x)))

Gráfico:

Definida a trozos:

Solución

Derivada de xsin(x)^(sin(xsin(x)))