Derivada de y=(cosx)^ctgx

Ha introducido [src]

   cot(x)   
cos      (x)

$$\cos^{\cot{\left(x \right)}}{\left(x \right)}$$

cos(x)^cot(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   cot(x)    //        2   \               cot(x)*sin(x)\
cos      (x)*|\-1 - cot (x)/*log(cos(x)) - -------------|
             \                                 cos(x)   /

$$\left(\left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(\cos{\left(x \right)} \right)} - \frac{\sin{\left(x \right)} \cot{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{\cot{\left(x \right)}}{\left(x \right)}$$

Simplificar

Segunda derivada [src]

             /                                           2               2               /       2   \                                            \
   cot(x)    |//       2   \               cot(x)*sin(x)\             sin (x)*cot(x)   2*\1 + cot (x)/*sin(x)     /       2   \                   |
cos      (x)*||\1 + cot (x)/*log(cos(x)) + -------------|  - cot(x) - -------------- + ---------------------- + 2*\1 + cot (x)/*cot(x)*log(cos(x))|
             |\                                cos(x)   /                   2                  cos(x)                                             |
             \                                                           cos (x)                                                                  /

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de y=(cosx)^ctgx

Gráfico:

Definida a trozos:

Solución