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x*e^x*atan(x)/log(x)^(5*x)

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  • Derivada de:
  • 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)
  • Derivada de u/v

  • Expresiones idénticas

  • x*e^x*atan(x)/log(x)^(cinco *x)
  • x multiplicar por e en el grado x multiplicar por arco tangente de gente de (x) dividir por logaritmo de (x) en el grado (5 multiplicar por x)
  • x multiplicar por e en el grado x multiplicar por arco tangente de gente de (x) dividir por logaritmo de (x) en el grado (cinco multiplicar por x)
  • x*ex*atan(x)/log(x)(5*x)
  • x*ex*atanx/logx5*x
  • xe^xatan(x)/log(x)^(5x)
  • xexatan(x)/log(x)(5x)
  • xexatanx/logx5x
  • xe^xatanx/logx^5x
  • x*e^x*atan(x) dividir por log(x)^(5*x)

  • Expresiones semejantes

  • x*e^x*arctan(x)/log(x)^(5*x)
  • x*e^x*arctanx/log(x)^(5*x)

  • Expresiones con funciones

  • Logaritmo log
  • log_4(8^x+2^x)
Derivada de la función/ log(x)/ x*e^x/ tan(x)/ x*e^x*atan(x)/log(x)^(5*x)

Derivada de x*e^x*atan(x)/log(x)^(5*x)

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

Gráfico:

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Solución

Ha introducido [src] 
   x        
x*E *atan(x)
------------
    5*x     
 log   (x)
exxatan⁡(x)log⁡(x)5x\frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5 x}} 
((x*E^x)*atan(x))/log(x)^(5*x)
Gráfica
02468-8-6-4-2-1010-5000000025000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
           /                          x \                                                     
   -5*x    |/ x      x\            x*e  |        -5*x    /    5                   \          x
log    (x)*|\E  + x*e /*atan(x) + ------| + x*log    (x)*|- ------ - 5*log(log(x))|*atan(x)*e 
           |                           2|                \  log(x)                /           
           \                      1 + x /
x(−5log⁡(log⁡(x))−5log⁡(x))exlog⁡(x)−5xatan⁡(x)+(xexx2+1+(ex+xex)atan⁡(x))log⁡(x)−5xx \left(- 5 \log{\left(\log{\left(x \right)} \right)} - \frac{5}{\log{\left(x \right)}}\right) e^{x} \log{\left(x \right)}^{- 5 x} \operatorname{atan}{\left(x \right)} + \left(\frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)}^{- 5 x}
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Segunda derivada [src] 
           /                                                                                                     /                                  1   \        \   
           |                                                                               2                     |                        2   1 - ------|        |   
   -5*x    |                     /  1                 \ /  x                     \      2*x      2*(1 + x)       |  /  1                 \        log(x)|        |  x
log    (x)*|(2 + x)*atan(x) - 10*|------ + log(log(x))|*|------ + (1 + x)*atan(x)| - --------- + --------- + 5*x*|5*|------ + log(log(x))|  - ----------|*atan(x)|*e 
           |                     \log(x)              / |     2                  |           2          2        \  \log(x)              /     x*log(x) /        |   
           |                                            \1 + x                   /   /     2\      1 + x                                                         |   
           \                                                                         \1 + x /                                                                    /
(−2x2(x2+1)2+5x(5(log⁡(log⁡(x))+1log⁡(x))2−1−1log⁡(x)xlog⁡(x))atan⁡(x)+2(x+1)x2+1+(x+2)atan⁡(x)−10(xx2+1+(x+1)atan⁡(x))(log⁡(log⁡(x))+1log⁡(x)))exlog⁡(x)−5x\left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + 5 x \left(5 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} - \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)} - 10 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)\right) e^{x} \log{\left(x \right)}^{- 5 x}
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Tercera derivada [src] 
           /                                                                                                                                                                                               /         2 \                                                                                                    \   
           |                                                                                                                                                                                               |      4*x  |       /                                      2                                            \        |   
           |                                                                                                       /                                  1   \                                            2*x*|-1 + ------|       |                               1 - -------      /      1   \ /  1                 \|        |   
           |                                            /                        2              \                  |                        2   1 - ------|                                                |          2|       |                           3          2      15*|1 - ------|*|------ + log(log(x))||        |   
   -5*x    |                     /  1                 \ |                     2*x      2*(1 + x)|   3*(2 + x)      |  /  1                 \        log(x)| /  x                     \   6*x*(1 + x)       \     1 + x /       |     /  1                 \        log (x)      \    log(x)/ \log(x)              /|        |  x
log    (x)*|(3 + x)*atan(x) - 15*|------ + log(log(x))|*|(2 + x)*atan(x) - --------- + ---------| + --------- + 15*|5*|------ + log(log(x))|  - ----------|*|------ + (1 + x)*atan(x)| - ----------- + ----------------- + 5*x*|- 25*|------ + log(log(x))|  + ----------- + --------------------------------------|*atan(x)|*e 
           |                     \log(x)              / |                          2          2 |          2       \  \log(x)              /     x*log(x) / |     2                  |            2                2           |     \log(x)              /      2                          x*log(x)               |        |   
           |                                            |                  /     2\      1 + x  |     1 + x                                                 \1 + x                   /    /     2\         /     2\            \                                x *log(x)                                          /        |   
           \                                            \                  \1 + x /             /                                                                                         \1 + x /         \1 + x /                                                                                                         /
(−6x(x+1)(x2+1)2+5x(−25(log⁡(log⁡(x))+1log⁡(x))3+15(1−1log⁡(x))(log⁡(log⁡(x))+1log⁡(x))xlog⁡(x)+1−2log⁡(x)2x2log⁡(x))atan⁡(x)+2x(4x2x2+1−1)(x2+1)2+3(x+2)x2+1+(x+3)atan⁡(x)+15(xx2+1+(x+1)atan⁡(x))(5(log⁡(log⁡(x))+1log⁡(x))2−1−1log⁡(x)xlog⁡(x))−15(log⁡(log⁡(x))+1log⁡(x))(−2x2(x2+1)2+2(x+1)x2+1+(x+2)atan⁡(x)))exlog⁡(x)−5x\left(- \frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} + 5 x \left(- 25 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + \frac{15 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}} + \frac{1 - \frac{2}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)} + \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)} + 15 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right) \left(5 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} - \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) - 15 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \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)\right) e^{x} \log{\left(x \right)}^{- 5 x}
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Gráfico
Derivada de x*e^x*atan(x)/log(x)^(5*x)
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