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xsinh(x)/(x-1)^2

Derivada de xsinh(x)/(x-1)^2

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Solución

Ha introducido [src]
x*sinh(x)
---------
        2
 (x - 1) 
$$\frac{x \sinh{\left(x \right)}}{\left(x - 1\right)^{2}}$$
(x*sinh(x))/(x - 1)^2
Gráfica
Primera derivada [src]
x*cosh(x) + sinh(x)   x*(2 - 2*x)*sinh(x)
------------------- + -------------------
             2                     4     
      (x - 1)               (x - 1)      
$$\frac{x \left(2 - 2 x\right) \sinh{\left(x \right)}}{\left(x - 1\right)^{4}} + \frac{x \cosh{\left(x \right)} + \sinh{\left(x \right)}}{\left(x - 1\right)^{2}}$$
Segunda derivada [src]
                        4*(x*cosh(x) + sinh(x))   6*x*sinh(x)
2*cosh(x) + x*sinh(x) - ----------------------- + -----------
                                 -1 + x                    2 
                                                   (-1 + x)  
-------------------------------------------------------------
                                  2                          
                          (-1 + x)                           
$$\frac{x \sinh{\left(x \right)} + \frac{6 x \sinh{\left(x \right)}}{\left(x - 1\right)^{2}} + 2 \cosh{\left(x \right)} - \frac{4 \left(x \cosh{\left(x \right)} + \sinh{\left(x \right)}\right)}{x - 1}}{\left(x - 1\right)^{2}}$$
Tercera derivada [src]
                        6*(2*cosh(x) + x*sinh(x))   18*(x*cosh(x) + sinh(x))   24*x*sinh(x)
3*sinh(x) + x*cosh(x) - ------------------------- + ------------------------ - ------------
                                  -1 + x                           2                    3  
                                                           (-1 + x)             (-1 + x)   
-------------------------------------------------------------------------------------------
                                                 2                                         
                                         (-1 + x)                                          
$$\frac{x \cosh{\left(x \right)} - \frac{24 x \sinh{\left(x \right)}}{\left(x - 1\right)^{3}} + 3 \sinh{\left(x \right)} - \frac{6 \left(x \sinh{\left(x \right)} + 2 \cosh{\left(x \right)}\right)}{x - 1} + \frac{18 \left(x \cosh{\left(x \right)} + \sinh{\left(x \right)}\right)}{\left(x - 1\right)^{2}}}{\left(x - 1\right)^{2}}$$
Gráfico
Derivada de xsinh(x)/(x-1)^2