Sr Examen

Otras calculadoras

y=arctg^3(ln(chx)+(1/2ch^2*x))
Derivada de la función/ y=arctg^3(ln(chx)+(1/2ch^2*x))

Derivada de y=arctg^3(ln(chx)+(1/2ch^2*x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     /                   2   \
    3|               cosh (x)|
atan |log(cosh(x)) + --------|
     \                  2    /
atan⁡3(log⁡(cosh⁡(x))+cosh⁡2(x)2)\operatorname{atan}^{3}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)} 
atan(log(cosh(x)) + cosh(x)^2/2)^3
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       /                   2   \                            
      2|               cosh (x)| /sinh(x)                  \
3*atan |log(cosh(x)) + --------|*|------- + cosh(x)*sinh(x)|
       \                  2    / \cosh(x)                  /
------------------------------------------------------------
                                            2               
                   /                   2   \                
                   |               cosh (x)|                
               1 + |log(cosh(x)) + --------|                
                   \                  2    /
3(sinh⁡(x)cosh⁡(x)+sinh⁡(x)cosh⁡(x))atan⁡2(log⁡(cosh⁡(x))+cosh⁡2(x)2)(log⁡(cosh⁡(x))+cosh⁡2(x)2)2+1\frac{3 \left(\sinh{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{\cosh{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2}\right)^{2} + 1}
Simplificar
Segunda derivada [src] 
   /                                                                                          2                                  2                                          /    2                  \\                              
   |                                                                       /   1             \      2         /   1             \      2    /    2                    \     |cosh (x)               ||                              
   |/                              2   \     /    2                  \   8*|------- + cosh(x)| *sinh (x)    4*|------- + cosh(x)| *sinh (x)*\cosh (x) + 2*log(cosh(x))/*atan|-------- + log(cosh(x))||     /    2                  \
   ||        2          2      sinh (x)|     |cosh (x)               |     \cosh(x)          /                \cosh(x)          /                                           \   2                   /|     |cosh (x)               |
12*||1 + cosh (x) + sinh (x) - --------|*atan|-------- + log(cosh(x))| + -------------------------------- - -----------------------------------------------------------------------------------------|*atan|-------- + log(cosh(x))|
   ||                              2   |     \   2                   /                                  2                                                               2                            |     \   2                   /
   |\                          cosh (x)/                                     /    2                    \                                     /    2                    \                             |                              
   \                                                                     4 + \cosh (x) + 2*log(cosh(x))/                                 4 + \cosh (x) + 2*log(cosh(x))/                             /                              
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                 2                                                                                                  
                                                                                                      /    2                    \                                                                                                   
                                                                                                  4 + \cosh (x) + 2*log(cosh(x))/
12((sinh⁡2(x)−sinh⁡2(x)cosh⁡2(x)+cosh⁡2(x)+1)atan⁡(log⁡(cosh⁡(x))+cosh⁡2(x)2)−4(2log⁡(cosh⁡(x))+cosh⁡2(x))(cosh⁡(x)+1cosh⁡(x))2sinh⁡2(x)atan⁡(log⁡(cosh⁡(x))+cosh⁡2(x)2)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4+8(cosh⁡(x)+1cosh⁡(x))2sinh⁡2(x)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4)atan⁡(log⁡(cosh⁡(x))+cosh⁡2(x)2)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4\frac{12 \left(\left(\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)} - \frac{4 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right) \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{2} \sinh^{2}{\left(x \right)} \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} + \frac{8 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{2} \sinh^{2}{\left(x \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4}\right) \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4}
Simplificar
Tercera derivada [src] 
   /                                                                                                                                                                                                  /                              2   \     /    2                  \                                                                                                       /    2                  \                                                 /                              2   \                                                                                               \        
   |                                                                                            3                                  3      /    2                  \               /   1             \ |        2          2      sinh (x)|     |cosh (x)               |                         3                                          /    2                  \         2|cosh (x)               | /   1             \ /    2                    \ |        2          2      sinh (x)|                         3                            2      /    2                  \         |        
   |                                                                         /   1             \      2         /   1             \      2|cosh (x)               |     2      12*|------- + cosh(x)|*|1 + cosh (x) + sinh (x) - --------|*atan|-------- + log(cosh(x))|      /   1             \      2    /    2                    \     |cosh (x)               |   6*atan |-------- + log(cosh(x))|*|------- + cosh(x)|*\cosh (x) + 2*log(cosh(x))/*|1 + cosh (x) + sinh (x) - --------|      /   1             \  /    2                    \      2|cosh (x)               |     2   |        
   |     /    2                  \ /                            2   \     16*|------- + cosh(x)| *sinh (x)    4*|------- + cosh(x)| *atan |-------- + log(cosh(x))|*sinh (x)      \cosh(x)          / |                              2   |     \   2                   /   48*|------- + cosh(x)| *sinh (x)*\cosh (x) + 2*log(cosh(x))/*atan|-------- + log(cosh(x))|          \   2                   / \cosh(x)          /                             |                              2   |   16*|------- + cosh(x)| *\cosh (x) + 2*log(cosh(x))/ *atan |-------- + log(cosh(x))|*sinh (x)|        
   |    2|cosh (x)               | |     1                  sinh (x)|        \cosh(x)          /                \cosh(x)          /       \   2                   /                                   \                          cosh (x)/                                    \cosh(x)          /                                           \   2                   /                                                                                    \                          cosh (x)/      \cosh(x)          /                                    \   2                   /         |        
24*|atan |-------- + log(cosh(x))|*|- ------- + 2*cosh(x) + --------| + ----------------------------------- - -------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------|*sinh(x)
   |     \   2                   / |  cosh(x)                   3   |                                     2                                                 2                                                                              2                                                                                            2                                                                                                         2                                                                                                           2                             |        
   |                               \                        cosh (x)/   /                               2\                       /    2                    \                                                    /    2                    \                                                           /                               2\                                                                               /    2                    \                                                                          /                               2\                              |        
   |                                                                    |    /    2                    \ |                   4 + \cosh (x) + 2*log(cosh(x))/                                                4 + \cosh (x) + 2*log(cosh(x))/                                                           |    /    2                    \ |                                                                           4 + \cosh (x) + 2*log(cosh(x))/                                                                          |    /    2                    \ |                              |        
   \                                                                    \4 + \cosh (x) + 2*log(cosh(x))/ /                                                                                                                                                                                            \4 + \cosh (x) + 2*log(cosh(x))/ /                                                                                                                                                                                    \4 + \cosh (x) + 2*log(cosh(x))/ /                              /        
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                  2                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                       /    2                    \                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                   4 + \cosh (x) + 2*log(cosh(x))/
24((sinh⁡2(x)cosh⁡3(x)+2cosh⁡(x)−1cosh⁡(x))atan⁡2(log⁡(cosh⁡(x))+cosh⁡2(x)2)−6(2log⁡(cosh⁡(x))+cosh⁡2(x))(cosh⁡(x)+1cosh⁡(x))(sinh⁡2(x)−sinh⁡2(x)cosh⁡2(x)+cosh⁡2(x)+1)atan⁡2(log⁡(cosh⁡(x))+cosh⁡2(x)2)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4−4(cosh⁡(x)+1cosh⁡(x))3sinh⁡2(x)atan⁡2(log⁡(cosh⁡(x))+cosh⁡2(x)2)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4+12(cosh⁡(x)+1cosh⁡(x))(sinh⁡2(x)−sinh⁡2(x)cosh⁡2(x)+cosh⁡2(x)+1)atan⁡(log⁡(cosh⁡(x))+cosh⁡2(x)2)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4+16(2log⁡(cosh⁡(x))+cosh⁡2(x))2(cosh⁡(x)+1cosh⁡(x))3sinh⁡2(x)atan⁡2(log⁡(cosh⁡(x))+cosh⁡2(x)2)((2log⁡(cosh⁡(x))+cosh⁡2(x))2+4)2−48(2log⁡(cosh⁡(x))+cosh⁡2(x))(cosh⁡(x)+1cosh⁡(x))3sinh⁡2(x)atan⁡(log⁡(cosh⁡(x))+cosh⁡2(x)2)((2log⁡(cosh⁡(x))+cosh⁡2(x))2+4)2+16(cosh⁡(x)+1cosh⁡(x))3sinh⁡2(x)((2log⁡(cosh⁡(x))+cosh⁡2(x))2+4)2)sinh⁡(x)(2log⁡(cosh⁡(x))+cosh⁡2(x))2+4\frac{24 \left(\left(\frac{\sinh^{2}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} + 2 \cosh{\left(x \right)} - \frac{1}{\cosh{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)} - \frac{6 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right) \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right) \left(\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1\right) \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} - \frac{4 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} + \frac{12 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right) \left(\sinh^{2}{\left(x \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + \cosh^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4} + \frac{16 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4\right)^{2}} - \frac{48 \left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right) \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)} \operatorname{atan}{\left(\log{\left(\cosh{\left(x \right)} \right)} + \frac{\cosh^{2}{\left(x \right)}}{2} \right)}}{\left(\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4\right)^{2}} + \frac{16 \left(\cosh{\left(x \right)} + \frac{1}{\cosh{\left(x \right)}}\right)^{3} \sinh^{2}{\left(x \right)}}{\left(\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4\right)^{2}}\right) \sinh{\left(x \right)}}{\left(2 \log{\left(\cosh{\left(x \right)} \right)} + \cosh^{2}{\left(x \right)}\right)^{2} + 4}
Simplificar
Gráfico
Derivada de y=arctg^3(ln(chx)+(1/2ch^2*x))
    © Sr Examen – Калькулятор