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(x*e^x*arctanx)/ln^5x

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de -17x^2 Derivada de -17x^2
  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)

  • Expresiones idénticas

  • (x*e^x*arctanx)/ln^5x
  • (x multiplicar por e en el grado x multiplicar por arc tangente de x) dividir por ln en el grado 5x
  • (x*ex*arctanx)/ln5x
  • x*ex*arctanx/ln5x
  • (x*e^x*arctanx)/ln⁵x
  • (xe^xarctanx)/ln^5x
  • (xexarctanx)/ln5x
  • xexarctanx/ln5x
  • xe^xarctanx/ln^5x
  • (x*e^x*arctanx) dividir por ln^5x
Derivada de la función/ ln^5x/ x*e^x/ arctan/ (x*e^x*arctanx)/ln^5x

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   x        
x*E *atan(x)
------------
     5      
  log (x)
exxatan⁡(x)log⁡(x)5\frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}} 
((x*E^x)*atan(x))/log(x)^5
Gráfica
02468-8-6-4-2-1010-2000000010000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                          x                
/ x      x\            x*e                 
\E  + x*e /*atan(x) + ------               
                           2              x
                      1 + x    5*atan(x)*e 
---------------------------- - ------------
             5                      6      
          log (x)                log (x)
xexx2+1+(ex+xex)atan⁡(x)log⁡(x)5−5exatan⁡(x)log⁡(x)6\frac{\frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}} - \frac{5 e^{x} \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{6}}
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Segunda derivada [src] 
/                                             /  x                     \                         \   
|                                          10*|------ + (1 + x)*atan(x)|     /      6   \        |   
|                        2                    |     2                  |   5*|1 + ------|*atan(x)|   
|                     2*x      2*(1 + x)      \1 + x                   /     \    log(x)/        |  x
|(2 + x)*atan(x) - --------- + --------- - ----------------------------- + ----------------------|*e 
|                          2          2               x*log(x)                    x*log(x)       |   
|                  /     2\      1 + x                                                           |   
\                  \1 + x /                                                                      /   
-----------------------------------------------------------------------------------------------------
                                                  5                                                  
                                               log (x)
(−2x2(x2+1)2+2(x+1)x2+1+(x+2)atan⁡(x)+5(1+6log⁡(x))atan⁡(x)xlog⁡(x)−10(xx2+1+(x+1)atan⁡(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{atan}{\left(x \right)} + \frac{5 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(x \right)}} - \frac{10 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right)}{x \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}
Simplificar
Tercera derivada [src] 
/                                 /                        2              \                                                                                                                   \   
|                                 |                     2*x      2*(1 + x)|                     /         2 \                                                                                 |   
|                              15*|(2 + x)*atan(x) - --------- + ---------|                     |      4*x  |      /      9         21  \              /      6   \ /  x                     \|   
|                                 |                          2          2 |                 2*x*|-1 + ------|   10*|1 + ------ + -------|*atan(x)   15*|1 + ------|*|------ + (1 + x)*atan(x)||   
|                                 |                  /     2\      1 + x  |                     |          2|      |    log(x)      2   |              \    log(x)/ |     2                  ||   
|                  3*(2 + x)      \                  \1 + x /             /   6*x*(1 + x)       \     1 + x /      \             log (x)/                           \1 + x                   /|  x
|(3 + x)*atan(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)atan⁡(x)−15(−2x2(x2+1)2+2(x+1)x2+1+(x+2)atan⁡(x))xlog⁡(x)+15(1+6log⁡(x))(xx2+1+(x+1)atan⁡(x))x2log⁡(x)−10(1+9log⁡(x)+21log⁡(x)2)atan⁡(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{atan}{\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{atan}{\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{atan}{\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{atan}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}
Simplificar
Gráfico
Derivada de (x*e^x*arctanx)/ln^5x
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