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arctg(cos(x))
Derivada de la función/ arctg/ cos(x)/ arctg(cos(x))

Derivada de arctg(cos(x))

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

Gráfico:

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Solución

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