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y=e^xsinh(x)÷cosh[(x-1)]^2

Derivada de y=e^xsinh(x)÷cosh[(x-1)]^2

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

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Solución

Ha introducido [src]
  x         
 E *sinh(x) 
------------
    2       
cosh (x - 1)
$$\frac{e^{x} \sinh{\left(x \right)}}{\cosh^{2}{\left(x - 1 \right)}}$$
(E^x*sinh(x))/cosh(x - 1)^2
Gráfica
Primera derivada [src]
         x    x              x                    
cosh(x)*e  + e *sinh(x)   2*e *sinh(x)*sinh(x - 1)
----------------------- - ------------------------
          2                         3             
      cosh (x - 1)              cosh (x - 1)      
$$\frac{e^{x} \sinh{\left(x \right)} + e^{x} \cosh{\left(x \right)}}{\cosh^{2}{\left(x - 1 \right)}} - \frac{2 e^{x} \sinh{\left(x \right)} \sinh{\left(x - 1 \right)}}{\cosh^{3}{\left(x - 1 \right)}}$$
Segunda derivada [src]
  //           2        \                                                                 \   
  ||     3*sinh (-1 + x)|           2*(cosh(x) + sinh(x))*sinh(-1 + x)                    |  x
2*||-1 + ---------------|*sinh(x) - ---------------------------------- + cosh(x) + sinh(x)|*e 
  ||          2         |                      cosh(-1 + x)                               |   
  \\      cosh (-1 + x) /                                                                 /   
----------------------------------------------------------------------------------------------
                                            2                                                 
                                        cosh (-1 + x)                                         
$$\frac{2 \left(\left(\frac{3 \sinh^{2}{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}} - 1\right) \sinh{\left(x \right)} - \frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh{\left(x - 1 \right)}}{\cosh{\left(x - 1 \right)}} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) e^{x}}{\cosh^{2}{\left(x - 1 \right)}}$$
Tercera derivada [src]
  /                                                                                                              /           2        \                     \   
  |                                                                                                              |     3*sinh (-1 + x)|                     |   
  |                                                                                                            4*|-2 + ---------------|*sinh(x)*sinh(-1 + x)|   
  |                          /           2        \                                                              |          2         |                     |   
  |                          |     3*sinh (-1 + x)|                       6*(cosh(x) + sinh(x))*sinh(-1 + x)     \      cosh (-1 + x) /                     |  x
2*|2*cosh(x) + 2*sinh(x) + 3*|-1 + ---------------|*(cosh(x) + sinh(x)) - ---------------------------------- - ---------------------------------------------|*e 
  |                          |          2         |                                  cosh(-1 + x)                               cosh(-1 + x)                |   
  \                          \      cosh (-1 + x) /                                                                                                         /   
----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             2                                                                                  
                                                                         cosh (-1 + x)                                                                          
$$\frac{2 \left(- \frac{4 \left(\frac{3 \sinh^{2}{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}} - 2\right) \sinh{\left(x \right)} \sinh{\left(x - 1 \right)}}{\cosh{\left(x - 1 \right)}} + 3 \left(\frac{3 \sinh^{2}{\left(x - 1 \right)}}{\cosh^{2}{\left(x - 1 \right)}} - 1\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) - \frac{6 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sinh{\left(x - 1 \right)}}{\cosh{\left(x - 1 \right)}} + 2 \sinh{\left(x \right)} + 2 \cosh{\left(x \right)}\right) e^{x}}{\cosh^{2}{\left(x - 1 \right)}}$$
Gráfico
Derivada de y=e^xsinh(x)÷cosh[(x-1)]^2