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(x*e^x*arctgx)/(ln5x)^5

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de x=3at/1+t^2
  • Derivada de x*10^x Derivada de x*10^x
  • Derivada de (tgx+4)' Derivada de (tgx+4)'
  • Derivada de x-1+(1/4)(2e*-x-1)² Derivada de x-1+(1/4)(2e*-x-1)²

  • Expresiones idénticas

  • (x*e^x*arctgx)/(ln cinco x)^5
  • (x multiplicar por e en el grado x multiplicar por arctgx) dividir por (ln5x) en el grado 5
  • (x multiplicar por e en el grado x multiplicar por arctgx) dividir por (ln cinco x) en el grado 5
  • (x*ex*arctgx)/(ln5x)5
  • x*ex*arctgx/ln5x5
  • (x*e^x*arctgx)/(ln5x)⁵
  • (xe^xarctgx)/(ln5x)^5
  • (xexarctgx)/(ln5x)5
  • xexarctgx/ln5x5
  • xe^xarctgx/ln5x^5
  • (x*e^x*arctgx) dividir por (ln5x)^5
Derivada de la función/ x*e^x/ arctg/ (x*e^x*arctgx)/(ln5x)^5

Derivada de (x*e^x*arctgx)/(ln5x)^5

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 (5*x)
exxacot⁡(x)log⁡(5x)5\frac{e^{x} x \operatorname{acot}{\left(x \right)}}{\log{\left(5 x \right)}^{5}} 
((x*E^x)*acot(x))/log(5*x)^5
Gráfica
02468-8-6-4-2-1010-20002000
Trazar el gráfico f(x)
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 (5*x)              log (5*x)
−xexx2+1+(ex+xex)acot⁡(x)log⁡(5x)5−5exacot⁡(x)log⁡(5x)6\frac{- \frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{acot}{\left(x \right)}}{\log{\left(5 x \right)}^{5}} - \frac{5 e^{x} \operatorname{acot}{\left(x \right)}}{\log{\left(5 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(5*x)/        |  x
|(2 + x)*acot(x) - --------- + --------- + ----------------------------- + ------------------------|*e 
|                         2            2             x*log(5*x)                   x*log(5*x)       |   
|                    1 + x     /     2\                                                            |   
\                              \1 + x /                                                            /   
-------------------------------------------------------------------------------------------------------
                                                  5                                                    
                                               log (5*x)
(2x2(x2+1)2−2(x+1)x2+1+(x+2)acot⁡(x)+5(1+6log⁡(5x))acot⁡(x)xlog⁡(5x)+10(xx2+1−(x+1)acot⁡(x))xlog⁡(5x))exlog⁡(5x)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(5 x \right)}}\right) \operatorname{acot}{\left(x \right)}}{x \log{\left(5 x \right)}} + \frac{10 \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(5 x \right)}}\right) e^{x}}{\log{\left(5 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(5*x)/ |     2                  |      |    log(5*x)      2     |        |   
|                  3*(2 + x)      \                              \1 + x / /       \     1 + x /   6*x*(1 + x)                     \1 + x                   /      \               log (5*x)/        |  x
|(3 + x)*acot(x) - --------- - -------------------------------------------- - ----------------- + ----------- - -------------------------------------------- - -------------------------------------|*e 
|                         2                     x*log(5*x)                                2                2                     2                                           2                      |   
|                    1 + x                                                        /     2\         /     2\                     x *log(5*x)                                 x *log(5*x)             |   
\                                                                                 \1 + x /         \1 + x /                                                                                         /   
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                  5                                                                                                     
                                                                                               log (5*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⁡(5x)−15(1+6log⁡(5x))(xx2+1−(x+1)acot⁡(x))x2log⁡(5x)−10(1+9log⁡(5x)+21log⁡(5x)2)acot⁡(x)x2log⁡(5x))exlog⁡(5x)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(5 x \right)}} - \frac{15 \left(1 + \frac{6}{\log{\left(5 x \right)}}\right) \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x^{2} \log{\left(5 x \right)}} - \frac{10 \left(1 + \frac{9}{\log{\left(5 x \right)}} + \frac{21}{\log{\left(5 x \right)}^{2}}\right) \operatorname{acot}{\left(x \right)}}{x^{2} \log{\left(5 x \right)}}\right) e^{x}}{\log{\left(5 x \right)}^{5}}
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Gráfico
Derivada de (x*e^x*arctgx)/(ln5x)^5
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