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y=x^2*arctg(cos^24x)

Derivada de y=x^2*arctg(cos^24x)

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

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Solución

Ha introducido [src]
 2     /   2     \
x *atan\cos (4*x)/
$$x^{2} \operatorname{atan}{\left(\cos^{2}{\left(4 x \right)} \right)}$$
x^2*atan(cos(4*x)^2)
Gráfica
Primera derivada [src]
                         2                  
        /   2     \   8*x *cos(4*x)*sin(4*x)
2*x*atan\cos (4*x)/ - ----------------------
                                 4          
                          1 + cos (4*x)     
$$- \frac{8 x^{2} \sin{\left(4 x \right)} \cos{\left(4 x \right)}}{\cos^{4}{\left(4 x \right)} + 1} + 2 x \operatorname{atan}{\left(\cos^{2}{\left(4 x \right)} \right)}$$
Segunda derivada [src]
  /        /                             4         2     \                                           \
  |      2 |   2           2        4*cos (4*x)*sin (4*x)|                                           |
  |  16*x *|cos (4*x) - sin (4*x) + ---------------------|                                           |
  |        |                                   4         |                                           |
  |        \                            1 + cos (4*x)    /   16*x*cos(4*x)*sin(4*x)       /   2     \|
2*|- ----------------------------------------------------- - ---------------------- + atan\cos (4*x)/|
  |                             4                                       4                            |
  \                      1 + cos (4*x)                           1 + cos (4*x)                       /
$$2 \left(- \frac{16 x^{2} \left(- \sin^{2}{\left(4 x \right)} + \cos^{2}{\left(4 x \right)} + \frac{4 \sin^{2}{\left(4 x \right)} \cos^{4}{\left(4 x \right)}}{\cos^{4}{\left(4 x \right)} + 1}\right)}{\cos^{4}{\left(4 x \right)} + 1} - \frac{16 x \sin{\left(4 x \right)} \cos{\left(4 x \right)}}{\cos^{4}{\left(4 x \right)} + 1} + \operatorname{atan}{\left(\cos^{2}{\left(4 x \right)} \right)}\right)$$
Tercera derivada [src]
   /       /                             4         2     \                               /          4              6         2             2         2     \                  \
   |       |   2           2        4*cos (4*x)*sin (4*x)|                             2 |     3*cos (4*x)    8*cos (4*x)*sin (4*x)   5*cos (4*x)*sin (4*x)|                  |
16*|- 12*x*|cos (4*x) - sin (4*x) + ---------------------| - 3*cos(4*x)*sin(4*x) + 32*x *|1 - ------------- - --------------------- + ---------------------|*cos(4*x)*sin(4*x)|
   |       |                                   4         |                               |           4                          2                4         |                  |
   |       \                            1 + cos (4*x)    /                               |    1 + cos (4*x)      /       4     \          1 + cos (4*x)    |                  |
   \                                                                                     \                       \1 + cos (4*x)/                           /                  /
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                                                                                        4                                                                                      
                                                                                 1 + cos (4*x)                                                                                 
$$\frac{16 \left(32 x^{2} \left(1 + \frac{5 \sin^{2}{\left(4 x \right)} \cos^{2}{\left(4 x \right)}}{\cos^{4}{\left(4 x \right)} + 1} - \frac{3 \cos^{4}{\left(4 x \right)}}{\cos^{4}{\left(4 x \right)} + 1} - \frac{8 \sin^{2}{\left(4 x \right)} \cos^{6}{\left(4 x \right)}}{\left(\cos^{4}{\left(4 x \right)} + 1\right)^{2}}\right) \sin{\left(4 x \right)} \cos{\left(4 x \right)} - 12 x \left(- \sin^{2}{\left(4 x \right)} + \cos^{2}{\left(4 x \right)} + \frac{4 \sin^{2}{\left(4 x \right)} \cos^{4}{\left(4 x \right)}}{\cos^{4}{\left(4 x \right)} + 1}\right) - 3 \sin{\left(4 x \right)} \cos{\left(4 x \right)}\right)}{\cos^{4}{\left(4 x \right)} + 1}$$
Gráfico
Derivada de y=x^2*arctg(cos^24x)