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x*exp(x-i*pi)^3*ch(x)/(x^2+pi^2)^3(-x)
Derivada de la función/ x*exp(x-i*pi)^3*ch(x)/(x^2+pi^2)^3(-x)

Derivada de x*exp(x-i*pi)^3*ch(x)/(x^2+pi^2)^3(-x)

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

Gráfico:

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Solución

Ha introducido [src] 
             3             
  / x - I*pi\              
x*\e        / *cosh(x)     
----------------------*(-x)
               3           
     / 2     2\            
     \x  + pi /
−xx(ex−iπ)3cosh⁡(x)(x2+π2)3- x \frac{x \left(e^{x - i \pi}\right)^{3} \cosh{\left(x \right)}}{\left(x^{2} + \pi^{2}\right)^{3}} 
(((x*exp(x - i*pi)^3)*cosh(x))/(x^2 + pi^2)^3)*(-x)
Gráfica
02468-8-6-4-2-1010-5000000000000050000000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    //           3           \                                                   \                    
    ||/ x - I*pi\         3*x|             /  3*x\              2 /  3*x\        |     /  3*x\        
    |\\e        /  - 3*x*e   /*cosh(x) + x*\-e   /*sinh(x)   6*x *\-e   /*cosh(x)|   x*\-e   /*cosh(x)
- x*|----------------------------------------------------- - --------------------| - -----------------
    |                               3                                      4     |                3   
    |                     / 2     2\                             / 2     2\      |      / 2     2\    
    \                     \x  + pi /                             \x  + pi /      /      \x  + pi /
−x(−6x2(−e3x)cosh⁡(x)(x2+π2)4+x(−e3x)sinh⁡(x)+(−3xe3x+(ex−iπ)3)cosh⁡(x)(x2+π2)3)−x(−e3x)cosh⁡(x)(x2+π2)3- x \left(- \frac{6 x^{2} \left(- e^{3 x}\right) \cosh{\left(x \right)}}{\left(x^{2} + \pi^{2}\right)^{4}} + \frac{x \left(- e^{3 x}\right) \sinh{\left(x \right)} + \left(- 3 x e^{3 x} + \left(e^{x - i \pi}\right)^{3}\right) \cosh{\left(x \right)}}{\left(x^{2} + \pi^{2}\right)^{3}}\right) - \frac{x \left(- e^{3 x}\right) \cosh{\left(x \right)}}{\left(x^{2} + \pi^{2}\right)^{3}}
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Segunda derivada [src] 
/  /                                                                                                   /          2  \        \                                                    \     
|  |                                                                                                   |       8*x   |        |                                                    |     
|  |                                                                                               6*x*|-1 + --------|*cosh(x)|                                                    |     
|  |                                                                                                   |       2    2|        |                                           2        |     
|  |                                                        12*x*(x*sinh(x) + (1 + 3*x)*cosh(x))       \     pi  + x /        |                                       12*x *cosh(x)|  3*x
|x*|x*cosh(x) + 2*(1 + 3*x)*sinh(x) + 3*(2 + 3*x)*cosh(x) - ------------------------------------ + ---------------------------| + 2*x*sinh(x) + 2*(1 + 3*x)*cosh(x) - -------------|*e   
|  |                                                                        2    2                             2    2         |                                            2    2  |     
\  \                                                                      pi  + x                            pi  + x          /                                          pi  + x   /     
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 3                                                                                       
                                                                                       /  2    2\                                                                                        
                                                                                       \pi  + x /
(−12x2cosh⁡(x)x2+π2+x(xcosh⁡(x)−12x(xsinh⁡(x)+(3x+1)cosh⁡(x))x2+π2+6x(8x2x2+π2−1)cosh⁡(x)x2+π2+2(3x+1)sinh⁡(x)+3(3x+2)cosh⁡(x))+2xsinh⁡(x)+2(3x+1)cosh⁡(x))e3x(x2+π2)3\frac{\left(- \frac{12 x^{2} \cosh{\left(x \right)}}{x^{2} + \pi^{2}} + x \left(x \cosh{\left(x \right)} - \frac{12 x \left(x \sinh{\left(x \right)} + \left(3 x + 1\right) \cosh{\left(x \right)}\right)}{x^{2} + \pi^{2}} + \frac{6 x \left(\frac{8 x^{2}}{x^{2} + \pi^{2}} - 1\right) \cosh{\left(x \right)}}{x^{2} + \pi^{2}} + 2 \left(3 x + 1\right) \sinh{\left(x \right)} + 3 \left(3 x + 2\right) \cosh{\left(x \right)}\right) + 2 x \sinh{\left(x \right)} + 2 \left(3 x + 1\right) \cosh{\left(x \right)}\right) e^{3 x}}{\left(x^{2} + \pi^{2}\right)^{3}}
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Tercera derivada [src] 
/  /                                                                                                                                               /          2  \                                         /          2  \        \                                                                                                         /          2  \        \     
|  |                                                                                                                                               |       8*x   |                                       2 |      10*x   |        |                                                                                                         |       8*x   |        |     
|  |                                                                                                                                            18*|-1 + --------|*(x*sinh(x) + (1 + 3*x)*cosh(x))   48*x *|-3 + --------|*cosh(x)|                                                                                                    18*x*|-1 + --------|*cosh(x)|     
|  |                                                                                                                                               |       2    2|                                         |       2    2|        |                                                                                                         |       2    2|        |     
|  |                                                                             18*x*(x*cosh(x) + 2*(1 + 3*x)*sinh(x) + 3*(2 + 3*x)*cosh(x))      \     pi  + x /                                         \     pi  + x /        |                                                             36*x*(x*sinh(x) + (1 + 3*x)*cosh(x))        \     pi  + x /        |  3*x
|x*|x*sinh(x) + 3*(1 + 3*x)*cosh(x) + 9*(2 + 3*x)*sinh(x) + 27*(1 + x)*cosh(x) - ------------------------------------------------------------ + -------------------------------------------------- - -----------------------------| + 3*x*cosh(x) + 6*(1 + 3*x)*sinh(x) + 9*(2 + 3*x)*cosh(x) - ------------------------------------ + ----------------------------|*e   
|  |                                                                                                         2    2                                                    2    2                                           2         |                                                                             2    2                             2    2          |     
|  |                                                                                                       pi  + x                                                   pi  + x                                  /  2    2\          |                                                                           pi  + x                            pi  + x           |     
\  \                                                                                                                                                                                                          \pi  + x /          /                                                                                                                                /     
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                         3                                                                                                                                                                               
                                                                                                                                                                               /  2    2\                                                                                                                                                                                
                                                                                                                                                                               \pi  + x /
(x(−48x2(10x2x2+π2−3)cosh⁡(x)(x2+π2)2+xsinh⁡(x)−18x(xcosh⁡(x)+2(3x+1)sinh⁡(x)+3(3x+2)cosh⁡(x))x2+π2+27(x+1)cosh⁡(x)+3(3x+1)cosh⁡(x)+9(3x+2)sinh⁡(x)+18(xsinh⁡(x)+(3x+1)cosh⁡(x))(8x2x2+π2−1)x2+π2)+3xcosh⁡(x)−36x(xsinh⁡(x)+(3x+1)cosh⁡(x))x2+π2+18x(8x2x2+π2−1)cosh⁡(x)x2+π2+6(3x+1)sinh⁡(x)+9(3x+2)cosh⁡(x))e3x(x2+π2)3\frac{\left(x \left(- \frac{48 x^{2} \left(\frac{10 x^{2}}{x^{2} + \pi^{2}} - 3\right) \cosh{\left(x \right)}}{\left(x^{2} + \pi^{2}\right)^{2}} + x \sinh{\left(x \right)} - \frac{18 x \left(x \cosh{\left(x \right)} + 2 \left(3 x + 1\right) \sinh{\left(x \right)} + 3 \left(3 x + 2\right) \cosh{\left(x \right)}\right)}{x^{2} + \pi^{2}} + 27 \left(x + 1\right) \cosh{\left(x \right)} + 3 \left(3 x + 1\right) \cosh{\left(x \right)} + 9 \left(3 x + 2\right) \sinh{\left(x \right)} + \frac{18 \left(x \sinh{\left(x \right)} + \left(3 x + 1\right) \cosh{\left(x \right)}\right) \left(\frac{8 x^{2}}{x^{2} + \pi^{2}} - 1\right)}{x^{2} + \pi^{2}}\right) + 3 x \cosh{\left(x \right)} - \frac{36 x \left(x \sinh{\left(x \right)} + \left(3 x + 1\right) \cosh{\left(x \right)}\right)}{x^{2} + \pi^{2}} + \frac{18 x \left(\frac{8 x^{2}}{x^{2} + \pi^{2}} - 1\right) \cosh{\left(x \right)}}{x^{2} + \pi^{2}} + 6 \left(3 x + 1\right) \sinh{\left(x \right)} + 9 \left(3 x + 2\right) \cosh{\left(x \right)}\right) e^{3 x}}{\left(x^{2} + \pi^{2}\right)^{3}}
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Gráfico
Derivada de x*exp(x-i*pi)^3*ch(x)/(x^2+pi^2)^3(-x)
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