Sr Examen

Derivada de y=(ctg3x)^(2e)^x

Función f() - derivada -er orden en el punto
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Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
          /     x\
          \(2*E) /
(cot(3*x))        
$$\cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
cot(3*x)^((2*E)^x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
          /     x\ /     x /          2     \                                \
          \(2*E) / |(2*E) *\-3 - 3*cot (3*x)/        x                       |
(cot(3*x))        *|------------------------- + (2*E) *log(2*E)*log(cot(3*x))|
                   \         cot(3*x)                                        /
$$\left(\frac{\left(2 e\right)^{x} \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right)}{\cot{\left(3 x \right)}} + \left(2 e\right)^{x} \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
Segunda derivada [src]
                          /                                                                        2                                              2                             \
                 /     x\ |                           /                            /       2     \\                                /       2     \      /       2     \         |
     x           \(2*E) / |           2             x |                          3*\1 + cot (3*x)/|       2                      9*\1 + cot (3*x)/    6*\1 + cot (3*x)/*log(2*E)|
(2*E) *(cot(3*x))        *|18 + 18*cot (3*x) + (2*E) *|-log(2*E)*log(cot(3*x)) + -----------------|  + log (2*E)*log(cot(3*x)) - ------------------ - --------------------------|
                          |                           \                               cot(3*x)    /                                     2                      cot(3*x)         |
                          \                                                                                                          cot (3*x)                                  /
$$\left(2 e\right)^{x} \left(\left(2 e\right)^{x} \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right)^{2} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)}}{\cot{\left(3 x \right)}} + \log{\left(2 e \right)}^{2} \log{\left(\cot{\left(3 x \right)} \right)} + 18 \cot^{2}{\left(3 x \right)} + 18\right) \cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
Tercera derivada [src]
                          /                                                                                3                                                    3                                                    2                     2                                                                                                 /                                                                2                             \\
                 /     x\ |                                   /                            /       2     \\                                      /       2     \                                      /       2     \       /       2     \                  2      /       2     \            /                            /       2     \\ |                                                 /       2     \      /       2     \         ||
     x           \(2*E) / |   3                           2*x |                          3*\1 + cot (3*x)/|        /       2     \            54*\1 + cot (3*x)/       /       2     \            108*\1 + cot (3*x)/    27*\1 + cot (3*x)/ *log(2*E)   9*log (2*E)*\1 + cot (3*x)/          x |                          3*\1 + cot (3*x)/| |            2           2                      9*\1 + cot (3*x)/    6*\1 + cot (3*x)/*log(2*E)||
(2*E) *(cot(3*x))        *|log (2*E)*log(cot(3*x)) - (2*E)   *|-log(2*E)*log(cot(3*x)) + -----------------|  - 108*\1 + cot (3*x)/*cot(3*x) - ------------------- + 54*\1 + cot (3*x)/*log(2*E) + -------------------- - ---------------------------- - --------------------------- + 3*(2*E) *|-log(2*E)*log(cot(3*x)) + -----------------|*|-18 - 18*cot (3*x) - log (2*E)*log(cot(3*x)) + ------------------ + --------------------------||
                          |                                   \                               cot(3*x)    /                                           3                                                 cot(3*x)                     2                            cot(3*x)                     \                               cot(3*x)    / |                                                      2                      cot(3*x)         ||
                          \                                                                                                                        cot (3*x)                                                                      cot (3*x)                                                                                                  \                                                   cot (3*x)                                  //
$$\left(2 e\right)^{x} \left(- \left(2 e\right)^{2 x} \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right)^{3} + 3 \left(2 e\right)^{x} \left(\frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)} \log{\left(\cot{\left(3 x \right)} \right)}\right) \left(\frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)}}{\cot{\left(3 x \right)}} - \log{\left(2 e \right)}^{2} \log{\left(\cot{\left(3 x \right)} \right)} - 18 \cot^{2}{\left(3 x \right)} - 18\right) - \frac{54 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{\cot^{3}{\left(3 x \right)}} + \frac{108 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot{\left(3 x \right)}} - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(2 e \right)}}{\cot^{2}{\left(3 x \right)}} - 108 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} + 54 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)} - \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 e \right)}^{2}}{\cot{\left(3 x \right)}} + \log{\left(2 e \right)}^{3} \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{\left(2 e\right)^{x}}{\left(3 x \right)}$$
Gráfico
Derivada de y=(ctg3x)^(2e)^x