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y=(e^(arctg5x))/(x^3+4)
Derivada de la función/ ctg5x/ x^3+4/ arctg/ y=(e^(arctg5x))/(x^3+4)

Derivada de y=(e^(arctg5x))/(x^3+4)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 atan(5*x)
E         
----------
   3      
  x  + 4
eatan⁡(5x)x3+4\frac{e^{\operatorname{atan}{\left(5 x \right)}}}{x^{3} + 4} 
E^atan(5*x)/(x^3 + 4)
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
     2  atan(5*x)          atan(5*x)    
  3*x *e                5*e             
- --------------- + --------------------
             2      /        2\ / 3    \
     / 3    \       \1 + 25*x /*\x  + 4/
     \x  + 4/
−3x2eatan⁡(5x)(x3+4)2+5eatan⁡(5x)(25x2+1)(x3+4)- \frac{3 x^{2} e^{\operatorname{atan}{\left(5 x \right)}}}{\left(x^{3} + 4\right)^{2}} + \frac{5 e^{\operatorname{atan}{\left(5 x \right)}}}{\left(25 x^{2} + 1\right) \left(x^{3} + 4\right)}
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Segunda derivada [src] 
/                                              /         3 \\           
|                                              |      3*x  ||           
|                                          6*x*|-1 + ------||           
|                              2               |          3||           
|  25*(-1 + 10*x)          30*x                \     4 + x /|  atan(5*x)
|- -------------- - -------------------- + -----------------|*e         
|              2    /        2\ /     3\              3     |           
|   /        2\     \1 + 25*x /*\4 + x /         4 + x      |           
\   \1 + 25*x /                                             /           
------------------------------------------------------------------------
                                      3                                 
                                 4 + x
(−30x2(25x2+1)(x3+4)+6x(3x3x3+4−1)x3+4−25(10x−1)(25x2+1)2)eatan⁡(5x)x3+4\frac{\left(- \frac{30 x^{2}}{\left(25 x^{2} + 1\right) \left(x^{3} + 4\right)} + \frac{6 x \left(\frac{3 x^{3}}{x^{3} + 4} - 1\right)}{x^{3} + 4} - \frac{25 \left(10 x - 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) e^{\operatorname{atan}{\left(5 x \right)}}}{x^{3} + 4}
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Tercera derivada [src] 
/    /        3          6  \                                                                                              \           
|    |    18*x       27*x   |       /                                    2 \         /         3 \                         |           
|  6*|1 - ------ + ---------|       |         1          30*x       200*x  |         |      3*x  |                         |           
|    |         3           2|   125*|-2 + --------- - --------- + ---------|    90*x*|-1 + ------|                         |           
|    |    4 + x    /     3\ |       |             2           2           2|         |          3|           2             |           
|    \             \4 + x / /       \     1 + 25*x    1 + 25*x    1 + 25*x /         \     4 + x /      225*x *(-1 + 10*x) |  atan(5*x)
|- -------------------------- + -------------------------------------------- + -------------------- + ---------------------|*e         
|                 3                                        2                   /        2\ /     3\              2         |           
|            4 + x                              /        2\                    \1 + 25*x /*\4 + x /   /        2\  /     3\|           
\                                               \1 + 25*x /                                           \1 + 25*x / *\4 + x //           
---------------------------------------------------------------------------------------------------------------------------------------
                                                                      3                                                                
                                                                 4 + x
(225x2(10x−1)(25x2+1)2(x3+4)+90x(3x3x3+4−1)(25x2+1)(x3+4)−6(27x6(x3+4)2−18x3x3+4+1)x3+4+125(200x225x2+1−30x25x2+1−2+125x2+1)(25x2+1)2)eatan⁡(5x)x3+4\frac{\left(\frac{225 x^{2} \left(10 x - 1\right)}{\left(25 x^{2} + 1\right)^{2} \left(x^{3} + 4\right)} + \frac{90 x \left(\frac{3 x^{3}}{x^{3} + 4} - 1\right)}{\left(25 x^{2} + 1\right) \left(x^{3} + 4\right)} - \frac{6 \left(\frac{27 x^{6}}{\left(x^{3} + 4\right)^{2}} - \frac{18 x^{3}}{x^{3} + 4} + 1\right)}{x^{3} + 4} + \frac{125 \left(\frac{200 x^{2}}{25 x^{2} + 1} - \frac{30 x}{25 x^{2} + 1} - 2 + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right) e^{\operatorname{atan}{\left(5 x \right)}}}{x^{3} + 4}
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Gráfico
Derivada de y=(e^(arctg5x))/(x^3+4)
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