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y=arctg(cos(2*x))

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

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

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Solución

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