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y=(sin(4x))/(arctg(5/x))
Derivada de la función/ sin(4x)/ arctg/ y=(sin(4x))/(arctg(5/x))

Derivada de y=(sin(4x))/(arctg(5/x))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
sin(4*x)
--------
    /5\ 
atan|-| 
    \x/
sin⁡(4x)atan⁡(5x)\frac{\sin{\left(4 x \right)}}{\operatorname{atan}{\left(\frac{5}{x} \right)}} 
sin(4*x)/atan(5/x)
Gráfica
02468-8-6-4-2-1010-2020
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Primera derivada [src] 
4*cos(4*x)        5*sin(4*x)     
---------- + --------------------
     /5\      2 /    25\     2/5\
 atan|-|     x *|1 + --|*atan |-|
     \x/        |     2|      \x/
                \    x /
4cos⁡(4x)atan⁡(5x)+5sin⁡(4x)x2(1+25x2)atan⁡2(5x)\frac{4 \cos{\left(4 x \right)}}{\operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{5 \sin{\left(4 x \right)}}{x^{2} \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}^{2}{\left(\frac{5}{x} \right)}}
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Segunda derivada [src] 
  /                                      /          25               5         \         \
  |                                    5*|-1 + ----------- + ------------------|*sin(4*x)|
  |                                      |      2 /    25\     /    25\     /5\|         |
  |                                      |     x *|1 + --|   x*|1 + --|*atan|-||         |
  |                                      |        |     2|     |     2|     \x/|         |
  |                  20*cos(4*x)         \        \    x /     \    x /        /         |
2*|-8*sin(4*x) + ------------------- + --------------------------------------------------|
  |               2 /    25\     /5\                   3 /    25\     /5\                |
  |              x *|1 + --|*atan|-|                  x *|1 + --|*atan|-|                |
  |                 |     2|     \x/                     |     2|     \x/                |
  \                 \    x /                             \    x /                        /
------------------------------------------------------------------------------------------
                                             /5\                                          
                                         atan|-|                                          
                                             \x/
2(−8sin⁡(4x)+20cos⁡(4x)x2(1+25x2)atan⁡(5x)+5(−1+5x(1+25x2)atan⁡(5x)+25x2(1+25x2))sin⁡(4x)x3(1+25x2)atan⁡(5x))atan⁡(5x)\frac{2 \left(- 8 \sin{\left(4 x \right)} + \frac{20 \cos{\left(4 x \right)}}{x^{2} \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{5 \left(-1 + \frac{5}{x \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{25}{x^{2} \left(1 + \frac{25}{x^{2}}\right)}\right) \sin{\left(4 x \right)}}{x^{3} \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}}\right)}{\operatorname{atan}{\left(\frac{5}{x} \right)}}
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Tercera derivada [src] 
  /                                       /        175           2500               30                     75                    750         \                                                               \
  |                                     5*|3 - ----------- + ------------ - ------------------ + --------------------- + --------------------|*sin(4*x)      /          25               5         \         |
  |                                       |     2 /    25\              2     /    25\     /5\              2                       2        |            60*|-1 + ----------- + ------------------|*cos(4*x)|
  |                                       |    x *|1 + --|    4 /    25\    x*|1 + --|*atan|-|    2 /    25\      2/5\    3 /    25\      /5\|               |      2 /    25\     /    25\     /5\|         |
  |                                       |       |     2|   x *|1 + --|      |     2|     \x/   x *|1 + --| *atan |-|   x *|1 + --| *atan|-||               |     x *|1 + --|   x*|1 + --|*atan|-||         |
  |                                       |       \    x /      |     2|      \    x /              |     2|       \x/      |     2|      \x/|               |        |     2|     |     2|     \x/|         |
  |                   120*sin(4*x)        \                     \    x /                            \    x /                \    x /         /               \        \    x /     \    x /        /         |
2*|-32*cos(4*x) - ------------------- + --------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------|
  |                2 /    25\     /5\                                                  4 /    25\     /5\                                                                  3 /    25\     /5\                |
  |               x *|1 + --|*atan|-|                                                 x *|1 + --|*atan|-|                                                                 x *|1 + --|*atan|-|                |
  |                  |     2|     \x/                                                    |     2|     \x/                                                                    |     2|     \x/                |
  \                  \    x /                                                            \    x /                                                                            \    x /                        /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                       /5\                                                                                                    
                                                                                                   atan|-|                                                                                                    
                                                                                                       \x/
2(−32cos⁡(4x)−120sin⁡(4x)x2(1+25x2)atan⁡(5x)+60(−1+5x(1+25x2)atan⁡(5x)+25x2(1+25x2))cos⁡(4x)x3(1+25x2)atan⁡(5x)+5(3−30x(1+25x2)atan⁡(5x)−175x2(1+25x2)+75x2(1+25x2)2atan⁡2(5x)+750x3(1+25x2)2atan⁡(5x)+2500x4(1+25x2)2)sin⁡(4x)x4(1+25x2)atan⁡(5x))atan⁡(5x)\frac{2 \left(- 32 \cos{\left(4 x \right)} - \frac{120 \sin{\left(4 x \right)}}{x^{2} \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{60 \left(-1 + \frac{5}{x \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{25}{x^{2} \left(1 + \frac{25}{x^{2}}\right)}\right) \cos{\left(4 x \right)}}{x^{3} \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{5 \left(3 - \frac{30}{x \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}} - \frac{175}{x^{2} \left(1 + \frac{25}{x^{2}}\right)} + \frac{75}{x^{2} \left(1 + \frac{25}{x^{2}}\right)^{2} \operatorname{atan}^{2}{\left(\frac{5}{x} \right)}} + \frac{750}{x^{3} \left(1 + \frac{25}{x^{2}}\right)^{2} \operatorname{atan}{\left(\frac{5}{x} \right)}} + \frac{2500}{x^{4} \left(1 + \frac{25}{x^{2}}\right)^{2}}\right) \sin{\left(4 x \right)}}{x^{4} \left(1 + \frac{25}{x^{2}}\right) \operatorname{atan}{\left(\frac{5}{x} \right)}}\right)}{\operatorname{atan}{\left(\frac{5}{x} \right)}}
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Gráfico
Derivada de y=(sin(4x))/(arctg(5/x))
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