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y=e^xsinhx÷cosh(x-1^2)
Derivada de la función/ y=e^x/ sinhx/ y=e^xsinhx÷cosh(x-1^2)

Derivada de y=e^xsinhx÷cosh(x-1^2)

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

Ha introducido [src] 
  x        
 E *sinh(x)
-----------
cosh(x - 1)
exsinh⁡(x)cosh⁡(x−1)\frac{e^{x} \sinh{\left(x \right)}}{\cosh{\left(x - 1 \right)}} 
(E^x*sinh(x))/cosh(x - 1)
Gráfica
02468-8-6-4-2-1010-50000100000
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Trazar el gráfico f'(x)
Primera derivada [src] 
         x    x            x                    
cosh(x)*e  + e *sinh(x)   e *sinh(x)*sinh(x - 1)
----------------------- - ----------------------
      cosh(x - 1)                  2            
                               cosh (x - 1)
exsinh⁡(x)+excosh⁡(x)cosh⁡(x−1)−exsinh⁡(x)sinh⁡(x−1)cosh⁡2(x−1)\frac{e^{x} \sinh{\left(x \right)} + e^{x} \cosh{\left(x \right)}}{\cosh{\left(x - 1 \right)}} - \frac{e^{x} \sinh{\left(x \right)} \sinh{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}}
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Segunda derivada [src] 
/                        /           2        \                                             \   
|                        |     2*sinh (-1 + x)|           2*(cosh(x) + sinh(x))*sinh(-1 + x)|  x
|2*cosh(x) + 2*sinh(x) + |-1 + ---------------|*sinh(x) - ----------------------------------|*e 
|                        |          2         |                      cosh(-1 + x)           |   
\                        \      cosh (-1 + x) /                                             /   
------------------------------------------------------------------------------------------------
                                          cosh(-1 + x)
((2sinh⁡2(x−1)cosh⁡2(x−1)−1)sinh⁡(x)−2(sinh⁡(x)+cosh⁡(x))sinh⁡(x−1)cosh⁡(x−1)+2sinh⁡(x)+2cosh⁡(x))excosh⁡(x−1)\frac{\left(\left(\frac{2 \sinh^{2}{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}} - 1\right) \sinh{\left(x \right)} - \frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh{\left(x - 1 \right)}}{\cosh{\left(x - 1 \right)}} + 2 \sinh{\left(x \right)} + 2 \cosh{\left(x \right)}\right) e^{x}}{\cosh{\left(x - 1 \right)}}
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Tercera derivada [src] 
/                                                                                                            /           2        \                     \   
|                                                                                                            |     6*sinh (-1 + x)|                     |   
|                                                                                                            |-5 + ---------------|*sinh(x)*sinh(-1 + x)|   
|                          /           2        \                                                            |          2         |                     |   
|                          |     2*sinh (-1 + x)|                       6*(cosh(x) + sinh(x))*sinh(-1 + x)   \      cosh (-1 + x) /                     |  x
|4*cosh(x) + 4*sinh(x) + 3*|-1 + ---------------|*(cosh(x) + sinh(x)) - ---------------------------------- - -------------------------------------------|*e 
|                          |          2         |                                  cosh(-1 + x)                              cosh(-1 + x)               |   
\                          \      cosh (-1 + x) /                                                                                                       /   
------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                        cosh(-1 + x)
(3(2sinh⁡2(x−1)cosh⁡2(x−1)−1)(sinh⁡(x)+cosh⁡(x))−(6sinh⁡2(x−1)cosh⁡2(x−1)−5)sinh⁡(x)sinh⁡(x−1)cosh⁡(x−1)−6(sinh⁡(x)+cosh⁡(x))sinh⁡(x−1)cosh⁡(x−1)+4sinh⁡(x)+4cosh⁡(x))excosh⁡(x−1)\frac{\left(3 \left(\frac{2 \sinh^{2}{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}} - 1\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) - \frac{\left(\frac{6 \sinh^{2}{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}} - 5\right) \sinh{\left(x \right)} \sinh{\left(x - 1 \right)}}{\cosh{\left(x - 1 \right)}} - \frac{6 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh{\left(x - 1 \right)}}{\cosh{\left(x - 1 \right)}} + 4 \sinh{\left(x \right)} + 4 \cosh{\left(x \right)}\right) e^{x}}{\cosh{\left(x - 1 \right)}}
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Gráfico
Derivada de y=e^xsinhx÷cosh(x-1^2)
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