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Derivada de y=arctg2x^2

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

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Solución

Ha introducido [src]
    2     
atan (2*x)
$$\operatorname{atan}^{2}{\left(2 x \right)}$$
atan(2*x)^2
Gráfica
Primera derivada [src]
4*atan(2*x)
-----------
         2 
  1 + 4*x  
$$\frac{4 \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada [src]
8*(1 - 4*x*atan(2*x))
---------------------
               2     
     /       2\      
     \1 + 4*x /      
$$\frac{8 \left(- 4 x \operatorname{atan}{\left(2 x \right)} + 1\right)}{\left(4 x^{2} + 1\right)^{2}}$$
Tercera derivada [src]
   /                            2          \
   |               6*x      16*x *atan(2*x)|
32*|-atan(2*x) - -------- + ---------------|
   |                    2              2   |
   \             1 + 4*x        1 + 4*x    /
--------------------------------------------
                          2                 
                /       2\                  
                \1 + 4*x /                  
$$\frac{32 \left(\frac{16 x^{2} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{6 x}{4 x^{2} + 1} - \operatorname{atan}{\left(2 x \right)}\right)}{\left(4 x^{2} + 1\right)^{2}}$$
Gráfico
Derivada de y=arctg2x^2