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Derivada de la función/ (xx-6x+8)/(cbrt((xxx-9xx+24x-18)^2))

Derivada de (xx-6x+8)/(cbrt((xxx-9xx+24x-18)^2))

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

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Solución

Ha introducido [src] 
          x*x - 6*x + 8          
---------------------------------
   ______________________________
3 /                            2 
\/  (x*x*x - 9*x*x + 24*x - 18)
(−6x+xx)+8((24x+(−x9x+xxx))−18)23\frac{\left(- 6 x + x x\right) + 8}{\sqrt[3]{\left(\left(24 x + \left(- x 9 x + x x x\right)\right) - 18\right)^{2}}} 
(x*x - 6*x + 8)/(((x*x)*x - 9*x*x + 24*x - 18)^2)^(1/3)
Primera derivada [src] 
                                                               /               2        \          
             -6 + 2*x                          (x*x - 6*x + 8)*\48 - 36*x + 4*x  + 2*x*x/          
--------------------------------- - ---------------------------------------------------------------
   ______________________________        ______________________________                            
3 /                            2      3 /                            2                             
\/  (x*x*x - 9*x*x + 24*x - 18)     3*\/  (x*x*x - 9*x*x + 24*x - 18)  *(x*x*x - 9*x*x + 24*x - 18)
2x−6((24x+(−x9x+xxx))−18)23−((−6x+xx)+8)(4x2−36x+2xx+48)3((24x+(−x9x+xxx))−18)((24x+(−x9x+xxx))−18)23\frac{2 x - 6}{\sqrt[3]{\left(\left(24 x + \left(- x 9 x + x x x\right)\right) - 18\right)^{2}}} - \frac{\left(\left(- 6 x + x x\right) + 8\right) \left(4 x^{2} - 36 x + 2 x x + 48\right)}{3 \left(\left(24 x + \left(- x 9 x + x x x\right)\right) - 18\right) \sqrt[3]{\left(\left(24 x + \left(- x 9 x + x x x\right)\right) - 18\right)^{2}}}
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Segunda derivada [src] 
  /    /                            2   \                                           \
  |    |              /     2      \    |                                           |
  |    |            5*\8 + x  - 6*x/    | /     2      \                            |
  |    |6 - 2*x + ----------------------|*\8 + x  - 6*x/                            |
  |    |                 3      2       |                             /     2      \|
  |    \          -18 + x  - 9*x  + 24*x/                  4*(-3 + x)*\8 + x  - 6*x/|
2*|1 + ------------------------------------------------- + -------------------------|
  |                         3      2                               3             2  |
  \                  -18 + x  - 9*x  + 24*x                  18 - x  - 24*x + 9*x   /
-------------------------------------------------------------------------------------
                                                     2/3                             
                             |       3      2       |                                
                             |-18 + x  - 9*x  + 24*x|
2(4(x−3)(x2−6x+8)−x3+9x2−24x+18+(−2x+5(x2−6x+8)2x3−9x2+24x−18+6)(x2−6x+8)x3−9x2+24x−18+1)∣x3−9x2+24x−18∣23\frac{2 \left(\frac{4 \left(x - 3\right) \left(x^{2} - 6 x + 8\right)}{- x^{3} + 9 x^{2} - 24 x + 18} + \frac{\left(- 2 x + \frac{5 \left(x^{2} - 6 x + 8\right)^{2}}{x^{3} - 9 x^{2} + 24 x - 18} + 6\right) \left(x^{2} - 6 x + 8\right)}{x^{3} - 9 x^{2} + 24 x - 18} + 1\right)}{\left|{x^{3} - 9 x^{2} + 24 x - 18}\right|^{\frac{2}{3}}}
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Tercera derivada [src] 
  /                        /                         3                                \                                                               \
  |                        |           /     2      \                   /     2      \|                             /                            2   \|
  |                        |        20*\8 + x  - 6*x/       15*(-3 + x)*\8 + x  - 6*x/| /     2      \              |              /     2      \    ||
  |                        |1 + ------------------------- - --------------------------|*\8 + x  - 6*x/              |            5*\8 + x  - 6*x/    ||
  |                        |                            2            3      2         |                  3*(-3 + x)*|6 - 2*x + ----------------------||
  |     /     2      \     |    /       3      2       \      -18 + x  - 9*x  + 24*x  |                             |                 3      2       ||
  |   3*\8 + x  - 6*x/     \    \-18 + x  - 9*x  + 24*x/                              /                             \          -18 + x  - 9*x  + 24*x/|
4*|--------------------- - --------------------------------------------------------------------------- + ---------------------------------------------|
  |      3             2                                     3      2                                                       3      2                  |
  \18 - x  - 24*x + 9*x                               -18 + x  - 9*x  + 24*x                                         -18 + x  - 9*x  + 24*x           /
-------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                      2/3                                                              
                                                              |       3      2       |                                                                 
                                                              |-18 + x  - 9*x  + 24*x|
4(3(x−3)(−2x+5(x2−6x+8)2x3−9x2+24x−18+6)x3−9x2+24x−18−(x2−6x+8)(−15(x−3)(x2−6x+8)x3−9x2+24x−18+20(x2−6x+8)3(x3−9x2+24x−18)2+1)x3−9x2+24x−18+3(x2−6x+8)−x3+9x2−24x+18)∣x3−9x2+24x−18∣23\frac{4 \left(\frac{3 \left(x - 3\right) \left(- 2 x + \frac{5 \left(x^{2} - 6 x + 8\right)^{2}}{x^{3} - 9 x^{2} + 24 x - 18} + 6\right)}{x^{3} - 9 x^{2} + 24 x - 18} - \frac{\left(x^{2} - 6 x + 8\right) \left(- \frac{15 \left(x - 3\right) \left(x^{2} - 6 x + 8\right)}{x^{3} - 9 x^{2} + 24 x - 18} + \frac{20 \left(x^{2} - 6 x + 8\right)^{3}}{\left(x^{3} - 9 x^{2} + 24 x - 18\right)^{2}} + 1\right)}{x^{3} - 9 x^{2} + 24 x - 18} + \frac{3 \left(x^{2} - 6 x + 8\right)}{- x^{3} + 9 x^{2} - 24 x + 18}\right)}{\left|{x^{3} - 9 x^{2} + 24 x - 18}\right|^{\frac{2}{3}}}
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