Derivada de y=arctg(cos5x)/√cos5x

Ha introducido [src]

atan(cos(5*x))
--------------
   __________ 
 \/ cos(5*x)

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

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

Gráfica

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Primera derivada [src]

           5*sin(5*x)            5*atan(cos(5*x))*sin(5*x)
- ---------------------------- + -------------------------
  /       2     \   __________              3/2           
  \1 + cos (5*x)/*\/ cos(5*x)          2*cos   (5*x)

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

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Segunda derivada [src]

   /               /          2      \                                 /         2     \               \
   |    __________ |     2*sin (5*x) |                                 |    3*sin (5*x)|               |
   |  \/ cos(5*x) *|1 + -------------|                                 |2 + -----------|*atan(cos(5*x))|
   |               |           2     |               2                 |        2      |               |
   |               \    1 + cos (5*x)/            sin (5*x)            \     cos (5*x) /               |
25*|- -------------------------------- - --------------------------- + --------------------------------|
   |                  2                  /       2     \    3/2                     __________         |
   \           1 + cos (5*x)             \1 + cos (5*x)/*cos   (5*x)            4*\/ cos(5*x)          /

25 \left(- \frac{\left(1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}\right) \sqrt{\cos{\left(5 x \right)}}}{\cos^{2}{\left(5 x \right)} + 1} + \frac{\left(\frac{3 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 2\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{4 \sqrt{\cos{\left(5 x \right)}}} - \frac{\sin^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \cos^{\frac{3}{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) |     |    3*sin (5*x)|   |     15*sin (5*x)|               |         
    |           2               2                          2     3*|1 + -------------|   3*|2 + -----------|   |14 + ------------|*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     \                8*cos(5*x)            |         
    \                      1 + cos (5*x)                           2*\1 + cos (5*x)/      4*\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)}{2 \left(\cos^{2}{\left(5 x \right)} + 1\right)} - \frac{3 \left(\frac{3 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 2\right)}{4 \left(\cos^{2}{\left(5 x \right)} + 1\right)} + \frac{\left(\frac{15 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 14\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{8 \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)}}{\sqrt{\cos{\left(5 x \right)}}}

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Derivada de y=arctg(cos5x)/√cos5x

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