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y=arctg(cos5x)/cos5x
y es igual a arctg( coseno de 5x) dividir por coseno de 5x
y=arctgcos5x/cos5x
y=arctg(cos5x) dividir por cos5x
Expresiones con funciones
arctg
arctg^2(1/x)

Derivada de la función/ arctg/ cos5x/ y=arctg(cos5x)/cos5x

Derivada de y=arctg(cos5x)/cos5x

Solución

Ha introducido [src]

atan(cos(5*x))
--------------
   cos(5*x)

\frac{\operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos{\left(5 x \right)}}

atan(cos(5*x))/cos(5*x)

Primera derivada [src]

         5*sin(5*x)          5*atan(cos(5*x))*sin(5*x)
- ------------------------ + -------------------------
  /       2     \                       2             
  \1 + cos (5*x)/*cos(5*x)           cos (5*x)

\frac{5 \sin{\left(5 x \right)} \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos^{2}{\left(5 x \right)}} - \frac{5 \sin{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \cos{\left(5 x \right)}}

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Segunda derivada [src]

   /            2         /         2     \                                           \
   |       2*sin (5*x)    |    2*sin (5*x)|                                           |
   |  1 + -------------   |1 + -----------|*atan(cos(5*x))                            |
   |             2        |        2      |                              2            |
   |      1 + cos (5*x)   \     cos (5*x) /                         2*sin (5*x)       |
25*|- ----------------- + -------------------------------- - -------------------------|
   |           2                      cos(5*x)               /       2     \    2     |
   \    1 + cos (5*x)                                        \1 + cos (5*x)/*cos (5*x)/

25 \left(- \frac{1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}}{\cos^{2}{\left(5 x \right)} + 1} + \frac{\left(\frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 1\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos{\left(5 x \right)}} - \frac{2 \sin^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \cos^{2}{\left(5 x \right)}}\right)

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Tercera derivada [src]

    /          2               2              2         2                                                                                      \         
    |     6*cos (5*x)     2*sin (5*x)    8*cos (5*x)*sin (5*x)     /          2      \     /         2     \   /         2     \               |         
    |1 - ------------- + ------------- - ---------------------     |     2*sin (5*x) |     |    2*sin (5*x)|   |    6*sin (5*x)|               |         
    |           2               2                          2     3*|1 + -------------|   3*|1 + -----------|   |5 + -----------|*atan(cos(5*x))|         
    |    1 + cos (5*x)   1 + cos (5*x)      /       2     \        |           2     |     |        2      |   |        2      |               |         
    |                                       \1 + cos (5*x)/        \    1 + cos (5*x)/     \     cos (5*x) /   \     cos (5*x) /               |         
125*|--------------------------------------------------------- - --------------------- - ------------------- + --------------------------------|*sin(5*x)
    |                             2                                         2                      2                       cos(5*x)            |         
    \                      1 + cos (5*x)                             1 + cos (5*x)          1 + cos (5*x)                                      /         
---------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         cos(5*x)

\frac{125 \left(- \frac{3 \left(1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}\right)}{\cos^{2}{\left(5 x \right)} + 1} - \frac{3 \left(\frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 1\right)}{\cos^{2}{\left(5 x \right)} + 1} + \frac{\left(\frac{6 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 5\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos{\left(5 x \right)}} + \frac{1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1} - \frac{6 \cos^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1} - \frac{8 \sin^{2}{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right)^{2}}}{\cos^{2}{\left(5 x \right)} + 1}\right) \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}}

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Gráfico

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Derivada de y=arctg(cos5x)/cos5x

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Solución