Sr Examen

Otras calculadoras

y=e^cos^xsen^x
Derivada de la función/ y=e^c/ y=e^cos^xsen^x

Derivada de y=e^cos^xsen^x

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 /             / x\\
 |             \x /|
 \(cos(sin(x)))    /
E
ecos⁡xx(sin⁡(x))e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} 
E^(cos(sin(x))^(x^x))
Solución detallada

  1. Sustituimos u=cos⁡xx(sin⁡(x))u = \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}.

  2. Derivado eue^{u} es.

  3. Luego se aplica una cadena de reglas. Multiplicamos por ddxcos⁡xx(sin⁡(x))\frac{d}{d x} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}:

    1. No logro encontrar los pasos en la búsqueda de esta derivada.

      Perola derivada

      (log⁡(xx)+1)(xx)xx\left(\log{\left(x^{x} \right)} + 1\right) \left(x^{x}\right)^{x^{x}}

    Como resultado de la secuencia de reglas:

    (log⁡(xx)+1)(xx)xxecos⁡xx(sin⁡(x))\left(\log{\left(x^{x} \right)} + 1\right) \left(x^{x}\right)^{x^{x}} e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}}

Respuesta:

(log⁡(xx)+1)(xx)xxecos⁡xx(sin⁡(x))\left(\log{\left(x^{x} \right)} + 1\right) \left(x^{x}\right)^{x^{x}} e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}}

Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                                              /             / x\\
             / x\ /                                    x                   \  |             \x /|
             \x / | x                                 x *cos(x)*sin(sin(x))|  \(cos(sin(x)))    /
(cos(sin(x)))    *|x *(1 + log(x))*log(cos(sin(x))) - ---------------------|*e                   
                  \                                        cos(sin(x))     /
(xx(log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−xxsin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))ecos⁡xx(sin⁡(x))cos⁡xx(sin⁡(x))\left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{x^{x} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}
Simplificar
Segunda derivada [src] 
                                                                                                                                                                                                                                                                                                              /             / x\\
                / x\ /                                                                                      2                                                                                           2              / x\                           2       2                                            \  |             \x /|
 x              \x / |     2      log(cos(sin(x)))    x /                                cos(x)*sin(sin(x))\                2                     x /                                cos(x)*sin(sin(x))\               \x /   sin(x)*sin(sin(x))   cos (x)*sin (sin(x))   2*(1 + log(x))*cos(x)*sin(sin(x))|  \(cos(sin(x)))    /
x *(cos(sin(x)))    *|- cos (x) + ---------------- + x *|(1 + log(x))*log(cos(sin(x))) - ------------------|  + (1 + log(x)) *log(cos(sin(x))) + x *|(1 + log(x))*log(cos(sin(x))) - ------------------| *(cos(sin(x)))     + ------------------ - -------------------- - ---------------------------------|*e                   
                     |                   x              \                                   cos(sin(x))    /                                        \                                   cos(sin(x))    /                         cos(sin(x))              2                          cos(sin(x))           |                     
                     \                                                                                                                                                                                                                                 cos (sin(x))                                        /
xx(xx((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))2cos⁡xx(sin⁡(x))+xx((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))2+(log⁡(x)+1)2log⁡(cos⁡(sin⁡(x)))−2(log⁡(x)+1)sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x))+sin⁡(x)sin⁡(sin⁡(x))cos⁡(sin⁡(x))−sin⁡2(sin⁡(x))cos⁡2(x)cos⁡2(sin⁡(x))−cos⁡2(x)+log⁡(cos⁡(sin⁡(x)))x)ecos⁡xx(sin⁡(x))cos⁡xx(sin⁡(x))x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{2} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)} + x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{2} + \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{2 \left(\log{\left(x \right)} + 1\right) \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - \cos^{2}{\left(x \right)} + \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         /             / x\\
                / x\ /                                                         3                                                                                                                                                           3                 x                             3                       3       3                                                                                                       /                                                                                        2       2                                            \                                                              3              / x\                                        2                           2       2                                          / x\                                                      /                                                                                        2       2                                            \                                            2                      \  |             \x /|
 x              \x / | 2*x /                                cos(x)*sin(sin(x))\                3                    log(cos(sin(x)))        2                                      2*x /                                cos(x)*sin(sin(x))\               2*x    cos(x)*sin(sin(x))   2*cos (x)*sin(sin(x))   2*cos (x)*sin (sin(x))   3*(1 + log(x))*log(cos(sin(x)))      x /                                cos(x)*sin(sin(x))\ |     2      log(cos(sin(x)))               2                    sin(x)*sin(sin(x))   cos (x)*sin (sin(x))   2*(1 + log(x))*cos(x)*sin(sin(x))|      2*x /                                cos(x)*sin(sin(x))\               \x /   3*cos(x)*sin(sin(x))   3*(1 + log(x)) *cos(x)*sin(sin(x))   3*cos (x)*sin (sin(x))*(1 + log(x))      x              \x / /                                cos(x)*sin(sin(x))\ |     2      log(cos(sin(x)))               2                    sin(x)*sin(sin(x))   cos (x)*sin (sin(x))   2*(1 + log(x))*cos(x)*sin(sin(x))|   3*(1 + log(x))*sin(x)*sin(sin(x))   3*sin (sin(x))*cos(x)*sin(x)|  \(cos(sin(x)))    /
x *(cos(sin(x)))    *|x   *|(1 + log(x))*log(cos(sin(x))) - ------------------|  + (1 + log(x)) *log(cos(sin(x))) - ---------------- - 3*cos (x)*(1 + log(x)) + 3*cos(x)*sin(x) + x   *|(1 + log(x))*log(cos(sin(x))) - ------------------| *(cos(sin(x)))     + ------------------ - --------------------- - ---------------------- + ------------------------------- + 3*x *|(1 + log(x))*log(cos(sin(x))) - ------------------|*|- cos (x) + ---------------- + (1 + log(x)) *log(cos(sin(x))) + ------------------ - -------------------- - ---------------------------------| + 3*x   *|(1 + log(x))*log(cos(sin(x))) - ------------------| *(cos(sin(x)))     - -------------------- - ---------------------------------- - ----------------------------------- + 3*x *(cos(sin(x)))    *|(1 + log(x))*log(cos(sin(x))) - ------------------|*|- cos (x) + ---------------- + (1 + log(x)) *log(cos(sin(x))) + ------------------ - -------------------- - ---------------------------------| + --------------------------------- + ----------------------------|*e                   
                     |     \                                   cos(sin(x))    /                                             2                                                          \                                   cos(sin(x))    /                         cos(sin(x))            cos(sin(x))                3                               x                       \                                   cos(sin(x))    / |                   x                                               cos(sin(x))              2                          cos(sin(x))           |          \                                   cos(sin(x))    /                         x*cos(sin(x))                  cos(sin(x))                              2                                             \                                   cos(sin(x))    / |                   x                                               cos(sin(x))              2                          cos(sin(x))           |              cos(sin(x))                         2                |                     
                     \                                                                                                     x                                                                                                                                                                                       cos (sin(x))                                                                                                    \                                                                                         cos (sin(x))                                        /                                                                                                                                                            cos (sin(x))                                                                                          \                                                                                         cos (sin(x))                                        /                                               cos (sin(x))        /
xx(x2x((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))3cos⁡2xx(sin⁡(x))+3x2x((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))3cos⁡xx(sin⁡(x))+x2x((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))3+3xx((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))((log⁡(x)+1)2log⁡(cos⁡(sin⁡(x)))−2(log⁡(x)+1)sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x))+sin⁡(x)sin⁡(sin⁡(x))cos⁡(sin⁡(x))−sin⁡2(sin⁡(x))cos⁡2(x)cos⁡2(sin⁡(x))−cos⁡2(x)+log⁡(cos⁡(sin⁡(x)))x)cos⁡xx(sin⁡(x))+3xx((log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))−sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x)))((log⁡(x)+1)2log⁡(cos⁡(sin⁡(x)))−2(log⁡(x)+1)sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x))+sin⁡(x)sin⁡(sin⁡(x))cos⁡(sin⁡(x))−sin⁡2(sin⁡(x))cos⁡2(x)cos⁡2(sin⁡(x))−cos⁡2(x)+log⁡(cos⁡(sin⁡(x)))x)+(log⁡(x)+1)3log⁡(cos⁡(sin⁡(x)))−3(log⁡(x)+1)2sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x))+3(log⁡(x)+1)sin⁡(x)sin⁡(sin⁡(x))cos⁡(sin⁡(x))−3(log⁡(x)+1)sin⁡2(sin⁡(x))cos⁡2(x)cos⁡2(sin⁡(x))−3(log⁡(x)+1)cos⁡2(x)+3sin⁡(x)sin⁡2(sin⁡(x))cos⁡(x)cos⁡2(sin⁡(x))+3sin⁡(x)cos⁡(x)−2sin⁡3(sin⁡(x))cos⁡3(x)cos⁡3(sin⁡(x))−2sin⁡(sin⁡(x))cos⁡3(x)cos⁡(sin⁡(x))+sin⁡(sin⁡(x))cos⁡(x)cos⁡(sin⁡(x))+3(log⁡(x)+1)log⁡(cos⁡(sin⁡(x)))x−3sin⁡(sin⁡(x))cos⁡(x)xcos⁡(sin⁡(x))−log⁡(cos⁡(sin⁡(x)))x2)ecos⁡xx(sin⁡(x))cos⁡xx(sin⁡(x))x^{x} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{3} \cos^{2 x^{x}}{\left(\sin{\left(x \right)} \right)} + 3 x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{3} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)} + x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right)^{3} + 3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{2 \left(\log{\left(x \right)} + 1\right) \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - \cos^{2}{\left(x \right)} + \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)} + 3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{2 \left(\log{\left(x \right)} + 1\right) \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - \cos^{2}{\left(x \right)} + \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x}\right) + \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)} - \frac{3 \left(\log{\left(x \right)} + 1\right)^{2} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{3 \left(\log{\left(x \right)} + 1\right) \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} - \frac{3 \left(\log{\left(x \right)} + 1\right) \sin^{2}{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{\cos^{2}{\left(\sin{\left(x \right)} \right)}} - 3 \left(\log{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} + \frac{3 \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 \sin{\left(x \right)} \cos{\left(x \right)} - \frac{2 \sin^{3}{\left(\sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\cos^{3}{\left(\sin{\left(x \right)} \right)}} - \frac{2 \sin{\left(\sin{\left(x \right)} \right)} \cos^{3}{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{\sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{\cos{\left(\sin{\left(x \right)} \right)}} + \frac{3 \left(\log{\left(x \right)} + 1\right) \log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x} - \frac{3 \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \cos{\left(\sin{\left(x \right)} \right)}} - \frac{\log{\left(\cos{\left(\sin{\left(x \right)} \right)} \right)}}{x^{2}}\right) e^{\cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}} \cos^{x^{x}}{\left(\sin{\left(x \right)} \right)}
Simplificar
Gráfico
Derivada de y=e^cos^xsen^x
    © Sr Examen – Калькулятор