Sr Examen

Otras calculadoras


y=(ctgx)^x-5

Derivada de y=(ctgx)^x-5

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
   x       
cot (x) - 5
$$\cot^{x}{\left(x \right)} - 5$$
cot(x)^x - 5
Solución detallada
  1. diferenciamos miembro por miembro:

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

      Perola derivada

    2. La derivada de una constante es igual a cero.

    Como resultado de:


Respuesta:

Gráfica
Primera derivada [src]
        /  /        2   \              \
   x    |x*\-1 - cot (x)/              |
cot (x)*|---------------- + log(cot(x))|
        \     cot(x)                   /
$$\left(\frac{x \left(- \cot^{2}{\left(x \right)} - 1\right)}{\cot{\left(x \right)}} + \log{\left(\cot{\left(x \right)} \right)}\right) \cot^{x}{\left(x \right)}$$
Segunda derivada [src]
        /                                2                                                  \
        |/                 /       2   \\                  /                  /       2   \\|
   x    ||               x*\1 + cot (x)/|    /       2   \ |         2      x*\1 + cot (x)/||
cot (x)*||-log(cot(x)) + ---------------|  - \1 + cot (x)/*|-2*x + ------ + ---------------||
        |\                    cot(x)    /                  |       cot(x)          2       ||
        \                                                  \                    cot (x)    //
$$\left(\left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right)^{2} - \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} - 2 x + \frac{2}{\cot{\left(x \right)}}\right)\right) \cot^{x}{\left(x \right)}$$
Tercera derivada [src]
        /                                    3                              2                                               3                                                                                                         2\
        |    /                 /       2   \\                  /       2   \                                   /       2   \                    /                 /       2   \\ /                  /       2   \\       /       2   \ |
   x    |    |               x*\1 + cot (x)/|         2      3*\1 + cot (x)/        /       2   \          2*x*\1 + cot (x)/      /       2   \ |               x*\1 + cot (x)/| |         2      x*\1 + cot (x)/|   4*x*\1 + cot (x)/ |
cot (x)*|6 - |-log(cot(x)) + ---------------|  + 6*cot (x) - ---------------- - 4*x*\1 + cot (x)/*cot(x) - ------------------ + 3*\1 + cot (x)/*|-log(cot(x)) + ---------------|*|-2*x + ------ + ---------------| + ------------------|
        |    \                    cot(x)    /                       2                                              3                            \                    cot(x)    / |       cot(x)          2       |         cot(x)      |
        \                                                        cot (x)                                        cot (x)                                                          \                    cot (x)    /                     /
$$\left(- \frac{2 x \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{\cot^{3}{\left(x \right)}} + \frac{4 x \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot{\left(x \right)}} - 4 x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} - 2 x + \frac{2}{\cot{\left(x \right)}}\right) - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 6 \cot^{2}{\left(x \right)} + 6\right) \cot^{x}{\left(x \right)}$$
Gráfico
Derivada de y=(ctgx)^x-5