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Derivada de la función/ arctan/ y=arctang2x-arctang^3(3x)

Derivada de y=arctang2x-arctang^3(3x)

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

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Solución

Ha introducido [src] 
                 3     
atan(g2)*x - atan (3*x)
$$x \operatorname{atan}{\left(g_{2} \right)} - \operatorname{atan}^{3}{\left(3 x \right)}$$ 
atan(g2)*x - atan(3*x)^3
Primera derivada [src] 
        2                
  9*atan (3*x)           
- ------------ + atan(g2)
           2             
    1 + 9*x
$$\operatorname{atan}{\left(g_{2} \right)} - \frac{9 \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1}$$
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Segunda derivada [src] 
54*(-1 + 3*x*atan(3*x))*atan(3*x)
---------------------------------
                     2           
           /       2\            
           \1 + 9*x /
$$\frac{54 \left(3 x \operatorname{atan}{\left(3 x \right)} - 1\right) \operatorname{atan}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2}}$$
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Tercera derivada [src] 
    /                            2     2                      \
    |    2           1       36*x *atan (3*x)   18*x*atan(3*x)|
162*|atan (3*x) - -------- - ---------------- + --------------|
    |                    2              2                 2   |
    \             1 + 9*x        1 + 9*x           1 + 9*x    /
---------------------------------------------------------------
                                    2                          
                          /       2\                           
                          \1 + 9*x /
$$\frac{162 \left(- \frac{36 x^{2} \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{18 x \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} + \operatorname{atan}^{2}{\left(3 x \right)} - \frac{1}{9 x^{2} + 1}\right)}{\left(9 x^{2} + 1\right)^{2}}$$
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