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y=ln(arctg(x/2)+cos^2(4x))
Derivada de la función/ (x/2)/ arctg/ cos^2/ y=ln(arctg(x/2)+cos^2(4x))

Derivada de y=ln(arctg(x/2)+cos^2(4x))

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

Gráfico:

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Solución

Ha introducido [src] 
   /    /x\      2     \
log|atan|-| + cos (4*x)|
   \    \2/            /
log⁡(cos⁡2(4x)+atan⁡(x2))\log{\left(\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} \right)} 
log(atan(x/2) + cos(4*x)^2)
Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    1                           
---------- - 8*cos(4*x)*sin(4*x)
  /     2\                      
  |    x |                      
2*|1 + --|                      
  \    4 /                      
--------------------------------
          /x\      2            
      atan|-| + cos (4*x)       
          \2/
−8sin⁡(4x)cos⁡(4x)+12(x24+1)cos⁡2(4x)+atan⁡(x2)\frac{- 8 \sin{\left(4 x \right)} \cos{\left(4 x \right)} + \frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}}{\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}}
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Segunda derivada [src] 
   /                                                                          2\
   |                                          /    1                         \ |
   |                                          |- ------ + 4*cos(4*x)*sin(4*x)| |
   |                                          |       2                      | |
   |       2             2            x       \  4 + x                       / |
-4*|- 8*sin (4*x) + 8*cos (4*x) + --------- + ---------------------------------|
   |                                      2             2            /x\       |
   |                              /     2\           cos (4*x) + atan|-|       |
   \                              \4 + x /                           \2/       /
--------------------------------------------------------------------------------
                                 2            /x\                               
                              cos (4*x) + atan|-|                               
                                              \2/
−4(x(x2+4)2+(4sin⁡(4x)cos⁡(4x)−1x2+4)2cos⁡2(4x)+atan⁡(x2)−8sin⁡2(4x)+8cos⁡2(4x))cos⁡2(4x)+atan⁡(x2)- \frac{4 \left(\frac{x}{\left(x^{2} + 4\right)^{2}} + \frac{\left(4 \sin{\left(4 x \right)} \cos{\left(4 x \right)} - \frac{1}{x^{2} + 4}\right)^{2}}{\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}} - 8 \sin^{2}{\left(4 x \right)} + 8 \cos^{2}{\left(4 x \right)}\right)}{\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}}
Simplificar
Tercera derivada [src] 
  /                                                3                                         /    1                         \ /       2             2            x    \\
  |                /    1                         \                                        6*|- ------ + 4*cos(4*x)*sin(4*x)|*|- 8*sin (4*x) + 8*cos (4*x) + ---------||
  |              4*|- ------ + 4*cos(4*x)*sin(4*x)|                                          |       2                      | |                                      2||
  |                |       2                      |          2                               \  4 + x                       / |                              /     2\ ||
  |      1         \  4 + x                       /       4*x                                                                 \                              \4 + x / /|
4*|- --------- - ----------------------------------- + --------- + 128*cos(4*x)*sin(4*x) - ----------------------------------------------------------------------------|
  |          2                               2                 3                                                          2            /x\                             |
  |  /     2\           /   2            /x\\          /     2\                                                        cos (4*x) + atan|-|                             |
  |  \4 + x /           |cos (4*x) + atan|-||          \4 + x /                                                                        \2/                             |
  \                     \                \2//                                                                                                                          /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             2            /x\                                                                           
                                                                          cos (4*x) + atan|-|                                                                           
                                                                                          \2/
4(4x2(x2+4)3−4(4sin⁡(4x)cos⁡(4x)−1x2+4)3(cos⁡2(4x)+atan⁡(x2))2−6(4sin⁡(4x)cos⁡(4x)−1x2+4)(x(x2+4)2−8sin⁡2(4x)+8cos⁡2(4x))cos⁡2(4x)+atan⁡(x2)+128sin⁡(4x)cos⁡(4x)−1(x2+4)2)cos⁡2(4x)+atan⁡(x2)\frac{4 \left(\frac{4 x^{2}}{\left(x^{2} + 4\right)^{3}} - \frac{4 \left(4 \sin{\left(4 x \right)} \cos{\left(4 x \right)} - \frac{1}{x^{2} + 4}\right)^{3}}{\left(\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}\right)^{2}} - \frac{6 \left(4 \sin{\left(4 x \right)} \cos{\left(4 x \right)} - \frac{1}{x^{2} + 4}\right) \left(\frac{x}{\left(x^{2} + 4\right)^{2}} - 8 \sin^{2}{\left(4 x \right)} + 8 \cos^{2}{\left(4 x \right)}\right)}{\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}} + 128 \sin{\left(4 x \right)} \cos{\left(4 x \right)} - \frac{1}{\left(x^{2} + 4\right)^{2}}\right)}{\cos^{2}{\left(4 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)}}
Simplificar
Gráfico
Derivada de y=ln(arctg(x/2)+cos^2(4x))
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