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(x*e^x*arctgx)/ln^5x
Derivada de la función/ ln^5x/ x*e^x/ arctg/ (x*e^x*arctgx)/ln^5x

Derivada de (x*e^x*arctgx)/ln^5x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   x        
x*E *acot(x)
------------
     5      
  log (x)
exxacot⁡(x)log⁡(x)5\frac{e^{x} x \operatorname{acot}{\left(x \right)}}{\log{\left(x \right)}^{5}} 
((x*E^x)*acot(x))/log(x)^5
Gráfica
02468-8-6-4-2-1010-2000000020000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                          x                
/ x      x\            x*e                 
\E  + x*e /*acot(x) - ------               
                           2              x
                      1 + x    5*acot(x)*e 
---------------------------- - ------------
             5                      6      
          log (x)                log (x)
−xexx2+1+(ex+xex)acot⁡(x)log⁡(x)5−5exacot⁡(x)log⁡(x)6\frac{- \frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{acot}{\left(x \right)}}{\log{\left(x \right)}^{5}} - \frac{5 e^{x} \operatorname{acot}{\left(x \right)}}{\log{\left(x \right)}^{6}}
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Segunda derivada [src] 
/                                             /  x                     \                         \   
|                                          10*|------ - (1 + x)*acot(x)|     /      6   \        |   
|                                    2        |     2                  |   5*|1 + ------|*acot(x)|   
|                  2*(1 + x)      2*x         \1 + x                   /     \    log(x)/        |  x
|(2 + x)*acot(x) - --------- + --------- + ----------------------------- + ----------------------|*e 
|                         2            2              x*log(x)                    x*log(x)       |   
|                    1 + x     /     2\                                                          |   
\                              \1 + x /                                                          /   
-----------------------------------------------------------------------------------------------------
                                                  5                                                  
                                               log (x)
(2x2(x2+1)2−2(x+1)x2+1+(x+2)acot⁡(x)+5(1+6log⁡(x))acot⁡(x)xlog⁡(x)+10(xx2+1−(x+1)acot⁡(x))xlog⁡(x))exlog⁡(x)5\frac{\left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{acot}{\left(x \right)} + \frac{5 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{acot}{\left(x \right)}}{x \log{\left(x \right)}} + \frac{10 \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}
Simplificar
Tercera derivada [src] 
/                                 /                                    2  \                                                                                                                   \   
|                                 |                  2*(1 + x)      2*x   |       /         2 \                                                                                               |   
|                              15*|(2 + x)*acot(x) - --------- + ---------|       |      4*x  |                    /      6   \ /  x                     \      /      9         21  \        |   
|                                 |                         2            2|   2*x*|-1 + ------|                 15*|1 + ------|*|------ - (1 + x)*acot(x)|   10*|1 + ------ + -------|*acot(x)|   
|                                 |                    1 + x     /     2\ |       |          2|                    \    log(x)/ |     2                  |      |    log(x)      2   |        |   
|                  3*(2 + x)      \                              \1 + x / /       \     1 + x /   6*x*(1 + x)                   \1 + x                   /      \             log (x)/        |  x
|(3 + x)*acot(x) - --------- - -------------------------------------------- - ----------------- + ----------- - ------------------------------------------ - ---------------------------------|*e 
|                         2                      x*log(x)                                 2                2                     2                                        2                   |   
|                    1 + x                                                        /     2\         /     2\                     x *log(x)                                x *log(x)            |   
\                                                                                 \1 + x /         \1 + x /                                                                                   /   
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                5                                                                                                 
                                                                                             log (x)
(6x(x+1)(x2+1)2−2x(4x2x2+1−1)(x2+1)2−3(x+2)x2+1+(x+3)acot⁡(x)−15(2x2(x2+1)2−2(x+1)x2+1+(x+2)acot⁡(x))xlog⁡(x)−15(1+6log⁡(x))(xx2+1−(x+1)acot⁡(x))x2log⁡(x)−10(1+9log⁡(x)+21log⁡(x)2)acot⁡(x)x2log⁡(x))exlog⁡(x)5\frac{\left(\frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{acot}{\left(x \right)} - \frac{15 \left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(x \right)}} - \frac{15 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x^{2} \log{\left(x \right)}} - \frac{10 \left(1 + \frac{9}{\log{\left(x \right)}} + \frac{21}{\log{\left(x \right)}^{2}}\right) \operatorname{acot}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}
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Gráfico
Derivada de (x*e^x*arctgx)/ln^5x
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