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y=sinh^-1(tanh(x))
Derivada de la función/ tanh(x)/ y=sin/ y=sinh^-1(tanh(x))

Derivada de y=sinh^-1(tanh(x))

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

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Solución

Ha introducido [src] 
      1      
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sinh(tanh(x))
1sinh⁡(tanh⁡(x))\frac{1}{\sinh{\left(\tanh{\left(x \right)} \right)}} 
1/sinh(tanh(x))
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /        2   \               
-\1 - tanh (x)/*cosh(tanh(x)) 
------------------------------
            2                 
        sinh (tanh(x))
−(1−tanh⁡2(x))cosh⁡(tanh⁡(x))sinh⁡2(tanh⁡(x))- \frac{\left(1 - \tanh^{2}{\left(x \right)}\right) \cosh{\left(\tanh{\left(x \right)} \right)}}{\sinh^{2}{\left(\tanh{\left(x \right)} \right)}}
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Segunda derivada [src] 
                /                                               2          /         2   \\
/         2   \ |        2      2*cosh(tanh(x))*tanh(x)   2*cosh (tanh(x))*\-1 + tanh (x)/|
\-1 + tanh (x)/*|1 - tanh (x) - ----------------------- + --------------------------------|
                |                    sinh(tanh(x))                     2                  |
                \                                                  sinh (tanh(x))         /
-------------------------------------------------------------------------------------------
                                       sinh(tanh(x))
(tanh⁡2(x)−1)(2(tanh⁡2(x)−1)cosh⁡2(tanh⁡(x))sinh⁡2(tanh⁡(x))−tanh⁡2(x)+1−2cosh⁡(tanh⁡(x))tanh⁡(x)sinh⁡(tanh⁡(x)))sinh⁡(tanh⁡(x))\frac{\left(\tanh^{2}{\left(x \right)} - 1\right) \left(\frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right) \cosh^{2}{\left(\tanh{\left(x \right)} \right)}}{\sinh^{2}{\left(\tanh{\left(x \right)} \right)}} - \tanh^{2}{\left(x \right)} + 1 - \frac{2 \cosh{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}}\right)}{\sinh{\left(\tanh{\left(x \right)} \right)}}
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Tercera derivada [src] 
                /                                             2                                                                                               2                                                           \
                |                              /         2   \                    /         2   \                       2                      /         2   \      3                   2          /         2   \        |
/         2   \ |  /         2   \           5*\-1 + tanh (x)/ *cosh(tanh(x))   2*\-1 + tanh (x)/*cosh(tanh(x))   4*tanh (x)*cosh(tanh(x))   6*\-1 + tanh (x)/ *cosh (tanh(x))   12*cosh (tanh(x))*\-1 + tanh (x)/*tanh(x)|
\-1 + tanh (x)/*|6*\-1 + tanh (x)/*tanh(x) - -------------------------------- + ------------------------------- + ------------------------ + --------------------------------- - -----------------------------------------|
                |                                     sinh(tanh(x))                      sinh(tanh(x))                 sinh(tanh(x))                       3                                       2                      |
                \                                                                                                                                      sinh (tanh(x))                          sinh (tanh(x))             /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                       sinh(tanh(x))
(tanh⁡2(x)−1)(−5(tanh⁡2(x)−1)2cosh⁡(tanh⁡(x))sinh⁡(tanh⁡(x))+6(tanh⁡2(x)−1)2cosh⁡3(tanh⁡(x))sinh⁡3(tanh⁡(x))+6(tanh⁡2(x)−1)tanh⁡(x)+2(tanh⁡2(x)−1)cosh⁡(tanh⁡(x))sinh⁡(tanh⁡(x))−12(tanh⁡2(x)−1)cosh⁡2(tanh⁡(x))tanh⁡(x)sinh⁡2(tanh⁡(x))+4cosh⁡(tanh⁡(x))tanh⁡2(x)sinh⁡(tanh⁡(x)))sinh⁡(tanh⁡(x))\frac{\left(\tanh^{2}{\left(x \right)} - 1\right) \left(- \frac{5 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \cosh{\left(\tanh{\left(x \right)} \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}} + \frac{6 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \cosh^{3}{\left(\tanh{\left(x \right)} \right)}}{\sinh^{3}{\left(\tanh{\left(x \right)} \right)}} + 6 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)} + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right) \cosh{\left(\tanh{\left(x \right)} \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}} - \frac{12 \left(\tanh^{2}{\left(x \right)} - 1\right) \cosh^{2}{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{\sinh^{2}{\left(\tanh{\left(x \right)} \right)}} + \frac{4 \cosh{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}}\right)}{\sinh{\left(\tanh{\left(x \right)} \right)}}
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Gráfico
Derivada de y=sinh^-1(tanh(x))
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