Sr Examen

Derivada de x/((ln(ch(x)))^a)

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

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Definida a trozos:

Solución

Ha introducido [src]
      x      
-------------
   a         
log (cosh(x))
$$\frac{x}{\log{\left(\cosh{\left(x \right)} \right)}^{a}}$$
x/log(cosh(x))^a
Primera derivada [src]
                       -a                 
      1         a*x*log  (cosh(x))*sinh(x)
------------- - --------------------------
   a               cosh(x)*log(cosh(x))   
log (cosh(x))                             
$$- \frac{a x \log{\left(\cosh{\left(x \right)} \right)}^{- a} \sinh{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)}} + \frac{1}{\log{\left(\cosh{\left(x \right)} \right)}^{a}}$$
Segunda derivada [src]
                 /  /         2                 2                        2        \            \
     -a          |  |     sinh (x)          sinh (x)               a*sinh (x)     |   2*sinh(x)|
a*log  (cosh(x))*|x*|-1 + -------- + --------------------- + ---------------------| - ---------|
                 |  |         2          2                       2                |    cosh(x) |
                 \  \     cosh (x)   cosh (x)*log(cosh(x))   cosh (x)*log(cosh(x))/            /
------------------------------------------------------------------------------------------------
                                          log(cosh(x))                                          
$$\frac{a \left(x \left(\frac{a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} + \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 1 + \frac{\sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}}\right) - \frac{2 \sinh{\left(x \right)}}{\cosh{\left(x \right)}}\right) \log{\left(\cosh{\left(x \right)} \right)}^{- a}}{\log{\left(\cosh{\left(x \right)} \right)}}$$
Tercera derivada [src]
                 /                                            /                                         2                  2                        2                 2     2                         2                       2        \                                \
                 |                                            |          3             3*a        2*sinh (x)         2*sinh (x)               3*sinh (x)             a *sinh (x)              3*a*sinh (x)            3*a*sinh (x)     |                                |
                 |                                          x*|-2 - ------------ - ------------ + ---------- + ---------------------- + --------------------- + ---------------------- + --------------------- + ----------------------|*sinh(x)                        |
                 |           2                  2             |     log(cosh(x))   log(cosh(x))        2           2       2                2                       2       2                2                       2       2         |                        2       |
     -a          |     3*sinh (x)         3*sinh (x)          \                                    cosh (x)    cosh (x)*log (cosh(x))   cosh (x)*log(cosh(x))   cosh (x)*log (cosh(x))   cosh (x)*log(cosh(x))   cosh (x)*log (cosh(x))/                3*a*sinh (x)    |
a*log  (cosh(x))*|-3 + ---------- + --------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------|
                 |          2           2                                                                                                         cosh(x)                                                                                              2                |
                 \      cosh (x)    cosh (x)*log(cosh(x))                                                                                                                                                                                          cosh (x)*log(cosh(x))/
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                               log(cosh(x))                                                                                                                              
$$\frac{a \left(\frac{3 a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} - \frac{x \left(\frac{a^{2} \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)}^{2} \cosh^{2}{\left(x \right)}} + \frac{3 a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} - \frac{3 a}{\log{\left(\cosh{\left(x \right)} \right)}} + \frac{3 a \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)}^{2} \cosh^{2}{\left(x \right)}} + \frac{2 \sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 2 + \frac{3 \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}} - \frac{3}{\log{\left(\cosh{\left(x \right)} \right)}} + \frac{2 \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)}^{2} \cosh^{2}{\left(x \right)}}\right) \sinh{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{3 \sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 3 + \frac{3 \sinh^{2}{\left(x \right)}}{\log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)}}\right) \log{\left(\cosh{\left(x \right)} \right)}^{- a}}{\log{\left(\cosh{\left(x \right)} \right)}}$$