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y=log(x+1)*arctg^2(x^3)
Derivada de la función/ ctg^2/ arctg/ y=log/ (x^3)/ (x+1)/ y=log(x+1)*arctg^2(x^3)

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

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

Ha introducido [src] 
               2/ 3\
log(x + 1)*atan \x /
log⁡(x+1)atan⁡2(x3)\log{\left(x + 1 \right)} \operatorname{atan}^{2}{\left(x^{3} \right)} 
log(x + 1)*atan(x^3)^2
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
    2/ 3\      2     / 3\           
atan \x /   6*x *atan\x /*log(x + 1)
--------- + ------------------------
  x + 1                   6         
                     1 + x
6x2log⁡(x+1)atan⁡(x3)x6+1+atan⁡2(x3)x+1\frac{6 x^{2} \log{\left(x + 1 \right)} \operatorname{atan}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{atan}^{2}{\left(x^{3} \right)}}{x + 1}
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Segunda derivada [src] 
                  /                 3       6     / 3\\                              
                  |      / 3\    3*x     6*x *atan\x /|                              
              6*x*|2*atan\x / + ------ - -------------|*log(1 + x)                   
      2/ 3\       |                  6            6   |                   2     / 3\ 
  atan \x /       \             1 + x        1 + x    /               12*x *atan\x / 
- --------- + ---------------------------------------------------- + ----------------
          2                               6                                  /     6\
   (1 + x)                           1 + x                           (1 + x)*\1 + x /
12x2atan⁡(x3)(x+1)(x6+1)+6x(−6x6atan⁡(x3)x6+1+3x3x6+1+2atan⁡(x3))log⁡(x+1)x6+1−atan⁡2(x3)(x+1)2\frac{12 x^{2} \operatorname{atan}{\left(x^{3} \right)}}{\left(x + 1\right) \left(x^{6} + 1\right)} + \frac{6 x \left(- \frac{6 x^{6} \operatorname{atan}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{3 x^{3}}{x^{6} + 1} + 2 \operatorname{atan}{\left(x^{3} \right)}\right) \log{\left(x + 1 \right)}}{x^{6} + 1} - \frac{\operatorname{atan}^{2}{\left(x^{3} \right)}}{\left(x + 1\right)^{2}}
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Tercera derivada [src] 
  /              /        9         3        6     / 3\       12     / 3\           \                                                                           \
  |              |    27*x       9*x     27*x *atan\x /   36*x  *atan\x /       / 3\|                                      /                 3       6     / 3\\|
  |            6*|- --------- + ------ - -------------- + --------------- + atan\x /|*log(1 + x)                           |      / 3\    3*x     6*x *atan\x /||
  |              |          2        6            6                  2              |                                  9*x*|2*atan\x / + ------ - -------------||
  |    2/ 3\     |  /     6\    1 + x        1 + x           /     6\               |                   2     / 3\         |                  6            6   ||
  |atan \x /     \  \1 + x /                                 \1 + x /               /                9*x *atan\x /         \             1 + x        1 + x    /|
2*|--------- + --------------------------------------------------------------------------------- - ----------------- + -----------------------------------------|
  |        3                                              6                                               2 /     6\                        /     6\            |
  \ (1 + x)                                          1 + x                                         (1 + x) *\1 + x /                (1 + x)*\1 + x /            /
2(−9x2atan⁡(x3)(x+1)2(x6+1)+9x(−6x6atan⁡(x3)x6+1+3x3x6+1+2atan⁡(x3))(x+1)(x6+1)+6(36x12atan⁡(x3)(x6+1)2−27x9(x6+1)2−27x6atan⁡(x3)x6+1+9x3x6+1+atan⁡(x3))log⁡(x+1)x6+1+atan⁡2(x3)(x+1)3)2 \left(- \frac{9 x^{2} \operatorname{atan}{\left(x^{3} \right)}}{\left(x + 1\right)^{2} \left(x^{6} + 1\right)} + \frac{9 x \left(- \frac{6 x^{6} \operatorname{atan}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{3 x^{3}}{x^{6} + 1} + 2 \operatorname{atan}{\left(x^{3} \right)}\right)}{\left(x + 1\right) \left(x^{6} + 1\right)} + \frac{6 \left(\frac{36 x^{12} \operatorname{atan}{\left(x^{3} \right)}}{\left(x^{6} + 1\right)^{2}} - \frac{27 x^{9}}{\left(x^{6} + 1\right)^{2}} - \frac{27 x^{6} \operatorname{atan}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{9 x^{3}}{x^{6} + 1} + \operatorname{atan}{\left(x^{3} \right)}\right) \log{\left(x + 1 \right)}}{x^{6} + 1} + \frac{\operatorname{atan}^{2}{\left(x^{3} \right)}}{\left(x + 1\right)^{3}}\right)
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Gráfico
Derivada de y=log(x+1)*arctg^2(x^3)
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