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Derivada de x*ln(a*x*sh(b/x))

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

Ha introducido [src]
     /        /b\\
x*log|a*x*sinh|-||
     \        \x//
$$x \log{\left(a x \sinh{\left(\frac{b}{x} \right)} \right)}$$
x*log((a*x)*sinh(b/x))
Primera derivada [src]
                    /b\                   
            a*b*cosh|-|                   
      /b\           \x/                   
a*sinh|-| - -----------                   
      \x/        x           /        /b\\
----------------------- + log|a*x*sinh|-||
             /b\             \        \x//
       a*sinh|-|                          
             \x/                          
$$\log{\left(a x \sinh{\left(\frac{b}{x} \right)} \right)} + \frac{- \frac{a b \cosh{\left(\frac{b}{x} \right)}}{x} + a \sinh{\left(\frac{b}{x} \right)}}{a \sinh{\left(\frac{b}{x} \right)}}$$
Segunda derivada [src]
                       /b\     /                  /b\\        
                 b*cosh|-|     |            b*cosh|-||        
           /b\         \x/     |      /b\         \x/|     /b\
 2   - sinh|-| + ---------   b*|- sinh|-| + ---------|*cosh|-|
b          \x/       x         \      \x/       x    /     \x/
-- - --------------------- - ---------------------------------
 2              /b\                            2/b\           
x           sinh|-|                      x*sinh |-|           
                \x/                             \x/           
--------------------------------------------------------------
                              x                               
$$\frac{\frac{b^{2}}{x^{2}} - \frac{b \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right) \cosh{\left(\frac{b}{x} \right)}}{x \sinh^{2}{\left(\frac{b}{x} \right)}} - \frac{\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}}{\sinh{\left(\frac{b}{x} \right)}}}{x}$$
Tercera derivada [src]
                  /b\             /                  /b\\                  /                  /b\\                         /                  /b\\
            b*cosh|-|             |            b*cosh|-||                  |            b*cosh|-||                         |            b*cosh|-||
      /b\         \x/           2 |      /b\         \x/|    3     /b\     |      /b\         \x/|     /b\      2     2/b\ |      /b\         \x/|
- sinh|-| + ---------      2   b *|- sinh|-| + ---------|   b *cosh|-|   b*|- sinh|-| + ---------|*cosh|-|   2*b *cosh |-|*|- sinh|-| + ---------|
      \x/       x       2*b       \      \x/       x    /          \x/     \      \x/       x    /     \x/             \x/ \      \x/       x    /
--------------------- - ---- + -------------------------- + ---------- + --------------------------------- - -------------------------------------
           /b\            2             2     /b\            3     /b\                     2/b\                            2     3/b\             
       sinh|-|           x             x *sinh|-|           x *sinh|-|               x*sinh |-|                           x *sinh |-|             
           \x/                                \x/                  \x/                      \x/                                   \x/             
--------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         2                                                                        
                                                                        x                                                                         
$$\frac{\frac{b^{3} \cosh{\left(\frac{b}{x} \right)}}{x^{3} \sinh{\left(\frac{b}{x} \right)}} + \frac{b^{2} \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right)}{x^{2} \sinh{\left(\frac{b}{x} \right)}} - \frac{2 b^{2} \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right) \cosh^{2}{\left(\frac{b}{x} \right)}}{x^{2} \sinh^{3}{\left(\frac{b}{x} \right)}} - \frac{2 b^{2}}{x^{2}} + \frac{b \left(\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}\right) \cosh{\left(\frac{b}{x} \right)}}{x \sinh^{2}{\left(\frac{b}{x} \right)}} + \frac{\frac{b \cosh{\left(\frac{b}{x} \right)}}{x} - \sinh{\left(\frac{b}{x} \right)}}{\sinh{\left(\frac{b}{x} \right)}}}{x^{2}}$$