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

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  • Derivada de:
  • Derivada de (3*sqrt(v)-2*v*e^v)/v Derivada de (3*sqrt(v)-2*v*e^v)/v
  • Derivada de ((1-x^2)^(1/2)-x)/((1-x^2)^(1/2)+x) Derivada de ((1-x^2)^(1/2)-x)/((1-x^2)^(1/2)+x)
  • Derivada de (1-5x)^4 Derivada de (1-5x)^4
  • Derivada de y=e× Derivada de y=e×

  • Expresiones idénticas

  • (x*e^x*arctg*x)/(ln^ cinco)*x
  • (x multiplicar por e en el grado x multiplicar por arctg multiplicar por x) dividir por (ln en el grado 5) multiplicar por x
  • (x multiplicar por e en el grado x multiplicar por arctg multiplicar por x) dividir por (ln en el grado cinco) multiplicar por x
  • (x*ex*arctg*x)/(ln5)*x
  • x*ex*arctg*x/ln5*x
  • (x*e^x*arctg*x)/(ln⁵)*x
  • (xe^xarctgx)/(ln^5)x
  • (xexarctgx)/(ln5)x
  • xexarctgx/ln5x
  • xe^xarctgx/ln^5x
  • (x*e^x*arctg*x) dividir por (ln^5)*x
Derivada de la función/ x*e^x/ arctg/ (x*e^x*arctg*x)/(ln^5)*x

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   x          
x*E *atan(x)  
------------*x
     5        
  log (x)
xexxatan⁡(x)log⁡(x)5x \frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}} 
(((x*E^x)*atan(x))/log(x)^5)*x
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|      x        
  |                      1 + x    5*atan(x)*e |   x*E *atan(x)
x*|---------------------------- - ------------| + ------------
  |             5                      6      |        5      
  \          log (x)                log (x)   /     log (x)
x(xexx2+1+(ex+xex)atan⁡(x)log⁡(x)5−5exatan⁡(x)log⁡(x)6)+exxatan⁡(x)log⁡(x)5x \left(\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}}\right) + \frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}}
Simplificar
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)/        |   10*atan(x)    2*x                      |  x
|x*|(2 + x)*atan(x) - --------- + --------- - ----------------------------- + ----------------------| - ---------- + ------ + 2*(1 + x)*atan(x)|*e 
|  |                          2          2               x*log(x)                    x*log(x)       |     log(x)          2                    |   
|  |                  /     2\      1 + x                                                           |                1 + x                     |   
\  \                  \1 + x /                                                                      /                                          /   
---------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         5                                                                         
                                                                      log (x)
(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))+2xx2+1+2(x+1)atan⁡(x)−10atan⁡(x)log⁡(x))exlog⁡(x)5\frac{\left(x \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) + \frac{2 x}{x^{2} + 1} + 2 \left(x + 1\right) \operatorname{atan}{\left(x \right)} - \frac{10 \operatorname{atan}{\left(x \right)}}{\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                     \|                                                  /  x                     \                          |   
|  |                                 |                          2          2 |                 2*x*|-1 + ------|   10*|1 + ------ + -------|*atan(x)   15*|1 + ------|*|------ + (1 + x)*atan(x)||                                               30*|------ + (1 + x)*atan(x)|      /      6   \        |   
|  |                                 |                  /     2\      1 + x  |                     |          2|      |    log(x)      2   |              \    log(x)/ |     2                  ||         2                                        |     2                  |   15*|1 + ------|*atan(x)|   
|  |                  3*(2 + x)      \                  \1 + x /             /   6*x*(1 + x)       \     1 + x /      \             log (x)/                           \1 + x                   /|      6*x                          6*(1 + x)      \1 + x                   /      \    log(x)/        |  x
|x*|(3 + x)*atan(x) + --------- - -------------------------------------------- - ----------- + ----------------- - --------------------------------- + ------------------------------------------| - --------- + 3*(2 + x)*atan(x) + --------- - ----------------------------- + -----------------------|*e 
|  |                         2                      x*log(x)                              2                2                    2                                       2                        |           2                              2               x*log(x)                     x*log(x)       |   
|  |                    1 + x                                                     /     2\         /     2\                    x *log(x)                               x *log(x)                 |   /     2\                          1 + x                                                            |   
\  \                                                                              \1 + x /         \1 + x /                                                                                      /   \1 + x /                                                                                           /   
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                     5                                                                                                                                                      
                                                                                                                                                  log (x)
(−6x2(x2+1)2+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))+6(x+1)x2+1+3(x+2)atan⁡(x)+15(1+6log⁡(x))atan⁡(x)xlog⁡(x)−30(xx2+1+(x+1)atan⁡(x))xlog⁡(x))exlog⁡(x)5\frac{\left(- \frac{6 x^{2}}{\left(x^{2} + 1\right)^{2}} + x \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) + \frac{6 \left(x + 1\right)}{x^{2} + 1} + 3 \left(x + 2\right) \operatorname{atan}{\left(x \right)} + \frac{15 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(x \right)}} - \frac{30 \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
Gráfico
Derivada de (x*e^x*arctg*x)/(ln^5)*x
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