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(x*x*x+4)^(3x)

Derivada de (x*x*x+4)^(3x)

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

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Solución

Ha introducido [src]
           3*x
(x*x*x + 4)   
(xxx+4)3x\left(x x x + 4\right)^{3 x}
((x*x)*x + 4)^(3*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (3x)3x(log(3x)+1)\left(3 x\right)^{3 x} \left(\log{\left(3 x \right)} + 1\right)


Respuesta:

(3x)3x(log(3x)+1)\left(3 x\right)^{3 x} \left(\log{\left(3 x \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-5e915e91
Primera derivada [src]
               /                       /   2      \\
           3*x |                   3*x*\2*x  + x*x/|
(x*x*x + 4)   *|3*log(x*x*x + 4) + ----------------|
               \                      x*x*x + 4    /
(xxx+4)3x(3x(2x2+xx)xxx+4+3log(xxx+4))\left(x x x + 4\right)^{3 x} \left(\frac{3 x \left(2 x^{2} + x x\right)}{x x x + 4} + 3 \log{\left(x x x + 4 \right)}\right)
Segunda derivada [src]
              /                             /        3 \\
              |                           2 |     3*x  ||
              |                      2   x *|4 - ------||
          3*x |/    3               \       |         3||
  /     3\    || 3*x        /     3\|       \    4 + x /|
9*\4 + x /   *||------ + log\4 + x /|  + ---------------|
              ||     3              |              3    |
              \\4 + x               /         4 + x     /
9(x3+4)3x(x2(3x3x3+4+4)x3+4+(3x3x3+4+log(x3+4))2)9 \left(x^{3} + 4\right)^{3 x} \left(\frac{x^{2} \left(- \frac{3 x^{3}}{x^{3} + 4} + 4\right)}{x^{3} + 4} + \left(\frac{3 x^{3}}{x^{3} + 4} + \log{\left(x^{3} + 4 \right)}\right)^{2}\right)
3-я производная [src]
              /                              /           6         3 \                                           \
              |                              |       18*x      27*x  |        /        3 \ /    3               \|
              |                            x*|-8 - --------- + ------|      2 |     3*x  | | 3*x        /     3\||
              |                        3     |             2        3|   9*x *|4 - ------|*|------ + log\4 + x /||
          3*x |  /    3               \      |     /     3\    4 + x |        |         3| |     3              ||
  /     3\    |  | 3*x        /     3\|      \     \4 + x /          /        \    4 + x / \4 + x               /|
9*\4 + x /   *|3*|------ + log\4 + x /|  - --------------------------- + ----------------------------------------|
              |  |     3              |                    3                                   3                 |
              \  \4 + x               /               4 + x                               4 + x                  /
9(x3+4)3x(9x2(3x3x3+4+4)(3x3x3+4+log(x3+4))x3+4x(18x6(x3+4)2+27x3x3+48)x3+4+3(3x3x3+4+log(x3+4))3)9 \left(x^{3} + 4\right)^{3 x} \left(\frac{9 x^{2} \left(- \frac{3 x^{3}}{x^{3} + 4} + 4\right) \left(\frac{3 x^{3}}{x^{3} + 4} + \log{\left(x^{3} + 4 \right)}\right)}{x^{3} + 4} - \frac{x \left(- \frac{18 x^{6}}{\left(x^{3} + 4\right)^{2}} + \frac{27 x^{3}}{x^{3} + 4} - 8\right)}{x^{3} + 4} + 3 \left(\frac{3 x^{3}}{x^{3} + 4} + \log{\left(x^{3} + 4 \right)}\right)^{3}\right)
Tercera derivada [src]
              /                              /           6         3 \                                           \
              |                              |       18*x      27*x  |        /        3 \ /    3               \|
              |                            x*|-8 - --------- + ------|      2 |     3*x  | | 3*x        /     3\||
              |                        3     |             2        3|   9*x *|4 - ------|*|------ + log\4 + x /||
          3*x |  /    3               \      |     /     3\    4 + x |        |         3| |     3              ||
  /     3\    |  | 3*x        /     3\|      \     \4 + x /          /        \    4 + x / \4 + x               /|
9*\4 + x /   *|3*|------ + log\4 + x /|  - --------------------------- + ----------------------------------------|
              |  |     3              |                    3                                   3                 |
              \  \4 + x               /               4 + x                               4 + x                  /
9(x3+4)3x(9x2(3x3x3+4+4)(3x3x3+4+log(x3+4))x3+4x(18x6(x3+4)2+27x3x3+48)x3+4+3(3x3x3+4+log(x3+4))3)9 \left(x^{3} + 4\right)^{3 x} \left(\frac{9 x^{2} \left(- \frac{3 x^{3}}{x^{3} + 4} + 4\right) \left(\frac{3 x^{3}}{x^{3} + 4} + \log{\left(x^{3} + 4 \right)}\right)}{x^{3} + 4} - \frac{x \left(- \frac{18 x^{6}}{\left(x^{3} + 4\right)^{2}} + \frac{27 x^{3}}{x^{3} + 4} - 8\right)}{x^{3} + 4} + 3 \left(\frac{3 x^{3}}{x^{3} + 4} + \log{\left(x^{3} + 4 \right)}\right)^{3}\right)
Gráfico
Derivada de (x*x*x+4)^(3x)