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Derivada de la función/ 1+x^2/ arccos/ sqrt(1+x^2)*arccos(a^x^3)

Derivada de sqrt(1+x^2)*arccos(a^x^3)

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

Gráfico:

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Solución

Ha introducido [src] 
   ________     / / 3\\
  /      2      | \x /|
\/  1 + x  *acos\a    /
x2+1acos⁡(ax3)\sqrt{x^{2} + 1} \operatorname{acos}{\left(a^{x^{3}} \right)} 
sqrt(1 + x^2)*acos(a^(x^3))
Primera derivada [src] 
      / / 3\\      / 3\       ________       
      | \x /|      \x /  2   /      2        
x*acos\a    /   3*a    *x *\/  1 + x  *log(a)
------------- - -----------------------------
    ________               ___________       
   /      2               /         3        
 \/  1 + x               /       2*x         
                       \/   1 - a
−3ax3x2x2+1log⁡(a)1−a2x3+xacos⁡(ax3)x2+1- \frac{3 a^{x^{3}} x^{2} \sqrt{x^{2} + 1} \log{\left(a \right)}}{\sqrt{1 - a^{2 x^{3}}}} + \frac{x \operatorname{acos}{\left(a^{x^{3}} \right)}}{\sqrt{x^{2} + 1}}
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Segunda derivada [src] 
 /                                                                                /                        3          \       \
 |                                                               / 3\    ________ |                     2*x   3       |       |
 |/        2  \     / / 3\\                                      \x /   /      2  |       3          3*a    *x *log(a)|       |
 ||       x   |     | \x /|                                 3*x*a    *\/  1 + x  *|2 + 3*x *log(a) - -----------------|*log(a)|
 ||-1 + ------|*acos\a    /           / 3\                                        |                               3   |       |
 ||          2|                       \x /  3                                     |                            2*x    |       |
 |\     1 + x /                    6*a    *x *log(a)                              \                      -1 + a       /       |
-|------------------------- + --------------------------- + ------------------------------------------------------------------|
 |          ________                          ___________                                ___________                          |
 |         /      2              ________    /         3                                /         3                           |
 |       \/  1 + x              /      2    /       2*x                                /       2*x                            |
 \                            \/  1 + x  *\/   1 - a                                 \/   1 - a                               /
−(6ax3x3log⁡(a)1−a2x3x2+1+3ax3xx2+1(−3a2x3x3log⁡(a)a2x3−1+3x3log⁡(a)+2)log⁡(a)1−a2x3+(x2x2+1−1)acos⁡(ax3)x2+1)- (\frac{6 a^{x^{3}} x^{3} \log{\left(a \right)}}{\sqrt{1 - a^{2 x^{3}}} \sqrt{x^{2} + 1}} + \frac{3 a^{x^{3}} x \sqrt{x^{2} + 1} \left(- \frac{3 a^{2 x^{3}} x^{3} \log{\left(a \right)}}{a^{2 x^{3}} - 1} + 3 x^{3} \log{\left(a \right)} + 2\right) \log{\left(a \right)}}{\sqrt{1 - a^{2 x^{3}}}} + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \operatorname{acos}{\left(a^{x^{3}} \right)}}{\sqrt{x^{2} + 1}})
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Tercera derivada [src] 
  /                                                /                                         3                     3                    3           \                                                                                                   \
  |                               / 3\    ________ |                                      2*x   6    2          2*x   3              4*x   6    2   |                     /                        3          \                                         |
  |                               \x /   /      2  |       6    2          3          36*a    *x *log (a)   18*a    *x *log(a)   27*a    *x *log (a)|             / 3\    |                     2*x   3       |                                         |
  |  /        2  \     / / 3\\   a    *\/  1 + x  *|2 + 9*x *log (a) + 18*x *log(a) - ------------------- - ------------------ + -------------------|*log(a)      \x /  2 |       3          3*a    *x *log(a)|             / 3\    /        2  \       |
  |  |       x   |     | \x /|                     |                                                3                    3                      2   |          3*a    *x *|2 + 3*x *log(a) - -----------------|*log(a)      \x /  2 |       x   |       |
  |x*|-1 + ------|*acos\a    /                     |                                             2*x                  2*x           /         3\    |                     |                               3   |          3*a    *x *|-1 + ------|*log(a)|
  |  |          2|                                 |                                       -1 + a               -1 + a              |      2*x |    |                     |                            2*x    |                     |          2|       |
  |  \     1 + x /                                 \                                                                                \-1 + a    /    /                     \                      -1 + a       /                     \     1 + x /       |
3*|--------------------------- - --------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------- + -------------------------------|
  |                3/2                                                                     ___________                                                                                       ___________                                   ___________  |
  |        /     2\                                                                       /         3                                                                           ________    /         3                       ________    /         3   |
  |        \1 + x /                                                                      /       2*x                                                                           /      2    /       2*x                       /      2    /       2*x    |
  \                                                                                    \/   1 - a                                                                            \/  1 + x  *\/   1 - a                        \/  1 + x  *\/   1 - a       /
3(3ax3x2(x2x2+1−1)log⁡(a)1−a2x3x2+1−3ax3x2(−3a2x3x3log⁡(a)a2x3−1+3x3log⁡(a)+2)log⁡(a)1−a2x3x2+1−ax3x2+1(27a4x3x6log⁡(a)2(a2x3−1)2−36a2x3x6log⁡(a)2a2x3−1−18a2x3x3log⁡(a)a2x3−1+9x6log⁡(a)2+18x3log⁡(a)+2)log⁡(a)1−a2x3+x(x2x2+1−1)acos⁡(ax3)(x2+1)32)3 \left(\frac{3 a^{x^{3}} x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right) \log{\left(a \right)}}{\sqrt{1 - a^{2 x^{3}}} \sqrt{x^{2} + 1}} - \frac{3 a^{x^{3}} x^{2} \left(- \frac{3 a^{2 x^{3}} x^{3} \log{\left(a \right)}}{a^{2 x^{3}} - 1} + 3 x^{3} \log{\left(a \right)} + 2\right) \log{\left(a \right)}}{\sqrt{1 - a^{2 x^{3}}} \sqrt{x^{2} + 1}} - \frac{a^{x^{3}} \sqrt{x^{2} + 1} \left(\frac{27 a^{4 x^{3}} x^{6} \log{\left(a \right)}^{2}}{\left(a^{2 x^{3}} - 1\right)^{2}} - \frac{36 a^{2 x^{3}} x^{6} \log{\left(a \right)}^{2}}{a^{2 x^{3}} - 1} - \frac{18 a^{2 x^{3}} x^{3} \log{\left(a \right)}}{a^{2 x^{3}} - 1} + 9 x^{6} \log{\left(a \right)}^{2} + 18 x^{3} \log{\left(a \right)} + 2\right) \log{\left(a \right)}}{\sqrt{1 - a^{2 x^{3}}}} + \frac{x \left(\frac{x^{2}}{x^{2} + 1} - 1\right) \operatorname{acos}{\left(a^{x^{3}} \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}}}\right)
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