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y=arctg^2(6x^3+1)

Derivada de y=arctg^2(6x^3+1)

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

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Solución

Ha introducido [src]
    2/   3    \
atan \6*x  + 1/
$$\operatorname{atan}^{2}{\left(6 x^{3} + 1 \right)}$$
atan(6*x^3 + 1)^2
Gráfica
Primera derivada [src]
    2     /   3    \
36*x *atan\6*x  + 1/
--------------------
                2   
      /   3    \    
  1 + \6*x  + 1/    
$$\frac{36 x^{2} \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1}$$
Segunda derivada [src]
     /         3            3 /       3\     /       3\                 \
     |      9*x         18*x *\1 + 6*x /*atan\1 + 6*x /       /       3\|
72*x*|--------------- - ------------------------------- + atan\1 + 6*x /|
     |              2                         2                         |
     |    /       3\                /       3\                          |
     \1 + \1 + 6*x /            1 + \1 + 6*x /                          /
-------------------------------------------------------------------------
                                           2                             
                                 /       3\                              
                             1 + \1 + 6*x /                              
$$\frac{72 x \left(- \frac{18 x^{3} \left(6 x^{3} + 1\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1} + \frac{9 x^{3}}{\left(6 x^{3} + 1\right)^{2} + 1} + \operatorname{atan}{\left(6 x^{3} + 1 \right)}\right)}{\left(6 x^{3} + 1\right)^{2} + 1}$$
Tercera derivada [src]
   /                                                                                                                    2                                \
   |         3             6 /       3\         6     /       3\        3 /       3\     /       3\         6 /       3\      /       3\                 |
   |     54*x         972*x *\1 + 6*x /    324*x *atan\1 + 6*x /   108*x *\1 + 6*x /*atan\1 + 6*x /   1296*x *\1 + 6*x / *atan\1 + 6*x /       /       3\|
72*|--------------- - ------------------ - --------------------- - -------------------------------- + ---------------------------------- + atan\1 + 6*x /|
   |              2                    2                    2                            2                                     2                         |
   |    /       3\    /              2\           /       3\                   /       3\                     /              2\                          |
   |1 + \1 + 6*x /    |    /       3\ |       1 + \1 + 6*x /               1 + \1 + 6*x /                     |    /       3\ |                          |
   \                  \1 + \1 + 6*x / /                                                                       \1 + \1 + 6*x / /                          /
----------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                   2                                                                      
                                                                         /       3\                                                                       
                                                                     1 + \1 + 6*x /                                                                       
$$\frac{72 \left(\frac{1296 x^{6} \left(6 x^{3} + 1\right)^{2} \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(\left(6 x^{3} + 1\right)^{2} + 1\right)^{2}} - \frac{972 x^{6} \left(6 x^{3} + 1\right)}{\left(\left(6 x^{3} + 1\right)^{2} + 1\right)^{2}} - \frac{324 x^{6} \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1} - \frac{108 x^{3} \left(6 x^{3} + 1\right) \operatorname{atan}{\left(6 x^{3} + 1 \right)}}{\left(6 x^{3} + 1\right)^{2} + 1} + \frac{54 x^{3}}{\left(6 x^{3} + 1\right)^{2} + 1} + \operatorname{atan}{\left(6 x^{3} + 1 \right)}\right)}{\left(6 x^{3} + 1\right)^{2} + 1}$$
Gráfico
Derivada de y=arctg^2(6x^3+1)