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y=arctg(tg^2x)
Derivada de la función/ tg^2x/ arctg/ y=arctg(tg^2x)

Derivada de y=arctg(tg^2x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /   2   \
atan\tan (x)/
$$\operatorname{atan}{\left(\tan^{2}{\left(x \right)} \right)}$$ 
atan(tan(x)^2)
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/         2   \       
\2 + 2*tan (x)/*tan(x)
----------------------
            4         
     1 + tan (x)
$$\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1}$$
Simplificar
Segunda derivada [src] 
                /                     4    /       2   \\
  /       2   \ |         2      4*tan (x)*\1 + tan (x)/|
2*\1 + tan (x)/*|1 + 3*tan (x) - -----------------------|
                |                             4         |
                \                      1 + tan (x)      /
---------------------------------------------------------
                              4                          
                       1 + tan (x)
$$\frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1} + 3 \tan^{2}{\left(x \right)} + 1\right)}{\tan^{4}{\left(x \right)} + 1}$$
Simplificar
Tercera derivada [src] 
                /                                                         2                          2        \       
                |                     4    /       2   \     /       2   \     2        /       2   \     6   |       
  /       2   \ |         2      6*tan (x)*\1 + tan (x)/   5*\1 + tan (x)/ *tan (x)   8*\1 + tan (x)/ *tan (x)|       
8*\1 + tan (x)/*|2 + 3*tan (x) - ----------------------- - ------------------------ + ------------------------|*tan(x)
                |                             4                         4                               2     |       
                |                      1 + tan (x)               1 + tan (x)               /       4   \      |       
                \                                                                          \1 + tan (x)/      /       
----------------------------------------------------------------------------------------------------------------------
                                                            4                                                         
                                                     1 + tan (x)
$$\frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{5 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{6}{\left(x \right)}}{\left(\tan^{4}{\left(x \right)} + 1\right)^{2}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1} + 3 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1}$$
Simplificar
Gráfico
Derivada de y=arctg(tg^2x)
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