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Derivada de la función/ tg(7x)/ (x+3)/ y=(ctg(7x))^sh(x+3)

Derivada de y=(ctg(7x))^sh(x+3)

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

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Solución

Ha introducido [src] 
   sinh(x + 3)     
cot           (7*x)
cot⁡sinh⁡(x+3)(7x)\cot^{\sinh{\left(x + 3 \right)}}{\left(7 x \right)} 
cot(7*x)^sinh(x + 3)
Solución detallada

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

    Perola derivada

    (log⁡(sinh⁡(x+3))+1)sinh⁡sinh⁡(x+3)(x+3)\left(\log{\left(\sinh{\left(x + 3 \right)} \right)} + 1\right) \sinh^{\sinh{\left(x + 3 \right)}}{\left(x + 3 \right)}

  2. Simplificamos:

    (log⁡(sinh⁡(x+3))+1)sinh⁡sinh⁡(x+3)(x+3)\left(\log{\left(\sinh{\left(x + 3 \right)} \right)} + 1\right) \sinh^{\sinh{\left(x + 3 \right)}}{\left(x + 3 \right)}

Respuesta:

(log⁡(sinh⁡(x+3))+1)sinh⁡sinh⁡(x+3)(x+3)\left(\log{\left(\sinh{\left(x + 3 \right)} \right)} + 1\right) \sinh^{\sinh{\left(x + 3 \right)}}{\left(x + 3 \right)}

Primera derivada [src] 
                    /                            /          2     \            \
   sinh(x + 3)      |                            \-7 - 7*cot (7*x)/*sinh(x + 3)|
cot           (7*x)*|cosh(x + 3)*log(cot(7*x)) + ------------------------------|
                    \                                       cot(7*x)           /
((−7cot⁡2(7x)−7)sinh⁡(x+3)cot⁡(7x)+log⁡(cot⁡(7x))cosh⁡(x+3))cot⁡sinh⁡(x+3)(7x)\left(\frac{\left(- 7 \cot^{2}{\left(7 x \right)} - 7\right) \sinh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} + \log{\left(\cot{\left(7 x \right)} \right)} \cosh{\left(x + 3 \right)}\right) \cot^{\sinh{\left(x + 3 \right)}}{\left(7 x \right)}
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Segunda derivada [src] 
                    /                                                            2                                                                                  2                                             \
                    |/                               /       2     \            \                                                                    /       2     \                   /       2     \            |
   sinh(3 + x)      ||                             7*\1 + cot (7*x)/*sinh(3 + x)|                                   /       2     \               49*\1 + cot (7*x)/ *sinh(3 + x)   14*\1 + cot (7*x)/*cosh(3 + x)|
cot           (7*x)*||-cosh(3 + x)*log(cot(7*x)) + -----------------------------|  + log(cot(7*x))*sinh(3 + x) + 98*\1 + cot (7*x)/*sinh(3 + x) - ------------------------------- - ------------------------------|
                    |\                                        cot(7*x)          /                                                                               2                              cot(7*x)           |
                    \                                                                                                                                        cot (7*x)                                            /
((7(cot⁡2(7x)+1)sinh⁡(x+3)cot⁡(7x)−log⁡(cot⁡(7x))cosh⁡(x+3))2−49(cot⁡2(7x)+1)2sinh⁡(x+3)cot⁡2(7x)+98(cot⁡2(7x)+1)sinh⁡(x+3)−14(cot⁡2(7x)+1)cosh⁡(x+3)cot⁡(7x)+log⁡(cot⁡(7x))sinh⁡(x+3))cot⁡sinh⁡(x+3)(7x)\left(\left(\frac{7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \sinh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} - \log{\left(\cot{\left(7 x \right)} \right)} \cosh{\left(x + 3 \right)}\right)^{2} - \frac{49 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \sinh{\left(x + 3 \right)}}{\cot^{2}{\left(7 x \right)}} + 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \sinh{\left(x + 3 \right)} - \frac{14 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cosh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} + \log{\left(\cot{\left(7 x \right)} \right)} \sinh{\left(x + 3 \right)}\right) \cot^{\sinh{\left(x + 3 \right)}}{\left(7 x \right)}
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Tercera derivada [src] 
                    /                                                              3                                                                                              /                                                                                                                 2            \                                                                                                    3                                  2                                                                    2            \
                    |  /                               /       2     \            \                                  /                               /       2     \            \ |                                                                 /       2     \                  /       2     \             |                                                                                     /       2     \                    /       2     \                   /       2     \                    /       2     \             |
   sinh(3 + x)      |  |                             7*\1 + cot (7*x)/*sinh(3 + x)|                                  |                             7*\1 + cot (7*x)/*sinh(3 + x)| |                                /       2     \               14*\1 + cot (7*x)/*cosh(3 + x)   49*\1 + cot (7*x)/ *sinh(3 + x)|       /       2     \                    /       2     \                        686*\1 + cot (7*x)/ *sinh(3 + x)   147*\1 + cot (7*x)/ *cosh(3 + x)   21*\1 + cot (7*x)/*sinh(3 + x)   1372*\1 + cot (7*x)/ *sinh(3 + x)|
cot           (7*x)*|- |-cosh(3 + x)*log(cot(7*x)) + -----------------------------|  + cosh(3 + x)*log(cot(7*x)) + 3*|-cosh(3 + x)*log(cot(7*x)) + -----------------------------|*|-log(cot(7*x))*sinh(3 + x) - 98*\1 + cot (7*x)/*sinh(3 + x) + ------------------------------ + -------------------------------| + 294*\1 + cot (7*x)/*cosh(3 + x) - 1372*\1 + cot (7*x)/*cot(7*x)*sinh(3 + x) - -------------------------------- - -------------------------------- - ------------------------------ + ---------------------------------|
                    |  \                                        cot(7*x)          /                                  \                                        cot(7*x)          / |                                                                         cot(7*x)                            2                |                                                                                               3                                  2                               cot(7*x)                           cot(7*x)            |
                    \                                                                                                                                                             \                                                                                                          cot (7*x)           /                                                                                            cot (7*x)                          cot (7*x)                                                                                 /
(−(7(cot⁡2(7x)+1)sinh⁡(x+3)cot⁡(7x)−log⁡(cot⁡(7x))cosh⁡(x+3))3+3(7(cot⁡2(7x)+1)sinh⁡(x+3)cot⁡(7x)−log⁡(cot⁡(7x))cosh⁡(x+3))(49(cot⁡2(7x)+1)2sinh⁡(x+3)cot⁡2(7x)−98(cot⁡2(7x)+1)sinh⁡(x+3)+14(cot⁡2(7x)+1)cosh⁡(x+3)cot⁡(7x)−log⁡(cot⁡(7x))sinh⁡(x+3))−686(cot⁡2(7x)+1)3sinh⁡(x+3)cot⁡3(7x)+1372(cot⁡2(7x)+1)2sinh⁡(x+3)cot⁡(7x)−147(cot⁡2(7x)+1)2cosh⁡(x+3)cot⁡2(7x)−1372(cot⁡2(7x)+1)cot⁡(7x)sinh⁡(x+3)+294(cot⁡2(7x)+1)cosh⁡(x+3)−21(cot⁡2(7x)+1)sinh⁡(x+3)cot⁡(7x)+log⁡(cot⁡(7x))cosh⁡(x+3))cot⁡sinh⁡(x+3)(7x)\left(- \left(\frac{7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \sinh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} - \log{\left(\cot{\left(7 x \right)} \right)} \cosh{\left(x + 3 \right)}\right)^{3} + 3 \left(\frac{7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \sinh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} - \log{\left(\cot{\left(7 x \right)} \right)} \cosh{\left(x + 3 \right)}\right) \left(\frac{49 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \sinh{\left(x + 3 \right)}}{\cot^{2}{\left(7 x \right)}} - 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \sinh{\left(x + 3 \right)} + \frac{14 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cosh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} - \log{\left(\cot{\left(7 x \right)} \right)} \sinh{\left(x + 3 \right)}\right) - \frac{686 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{3} \sinh{\left(x + 3 \right)}}{\cot^{3}{\left(7 x \right)}} + \frac{1372 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \sinh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} - \frac{147 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \cosh{\left(x + 3 \right)}}{\cot^{2}{\left(7 x \right)}} - 1372 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)} \sinh{\left(x + 3 \right)} + 294 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cosh{\left(x + 3 \right)} - \frac{21 \left(\cot^{2}{\left(7 x \right)} + 1\right) \sinh{\left(x + 3 \right)}}{\cot{\left(7 x \right)}} + \log{\left(\cot{\left(7 x \right)} \right)} \cosh{\left(x + 3 \right)}\right) \cot^{\sinh{\left(x + 3 \right)}}{\left(7 x \right)}
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