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Derivada de la función/ x((x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))

Derivada de x((x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     __________________
  3 /                2 
x*\/  (x - 1)*(x + 2)  
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    (x - 1)*(x + 2)
x(x−1)(x+2)23(x−1)(x+2)\frac{x \sqrt[3]{\left(x - 1\right) \left(x + 2\right)^{2}}}{\left(x - 1\right) \left(x + 2\right)} 
(x*((x - 1)*(x + 2)^2)^(1/3))/(((x - 1)*(x + 2)))
Primera derivada [src] 
                /                                     /       2                    \\                                    
                |                                 2/3 |(x + 2)    (4 + 2*x)*(x - 1)||                                    
                |   __________________   x*|x + 2|   *|-------- + -----------------||     3 _______        2/3           
       1        |3 /                2                 \   3               3        /|   x*\/ x - 1 *|x + 2|   *(-1 - 2*x)
---------------*|\/  (x - 1)*(x + 2)   + -------------------------------------------| + ---------------------------------
(x - 1)*(x + 2) |                                           2/3        2            |                  2        2        
                \                                    (x - 1)   *(x + 2)             /           (x - 1) *(x + 2)
xx−13∣x+2∣23(−2x−1)(x−1)2(x+2)2+1(x−1)(x+2)(x((x−1)(2x+4)3+(x+2)23)∣x+2∣23(x−1)23(x+2)2+(x−1)(x+2)23)\frac{x \sqrt[3]{x - 1} \left|{x + 2}\right|^{\frac{2}{3}} \left(- 2 x - 1\right)}{\left(x - 1\right)^{2} \left(x + 2\right)^{2}} + \frac{1}{\left(x - 1\right) \left(x + 2\right)} \left(\frac{x \left(\frac{\left(x - 1\right) \left(2 x + 4\right)}{3} + \frac{\left(x + 2\right)^{2}}{3}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)^{2}} + \sqrt[3]{\left(x - 1\right) \left(x + 2\right)^{2}}\right)
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Segunda derivada [src] 
  /                 /        2/3     3 ________            \                                                              \                                                                                                                                 
  |                 | |2 + x|      2*\/ -1 + x *sign(2 + x)|                                                              |                                                                                                                                 
  |               x*|----------- + ------------------------|                                                              |                                                                                                                                 
  |         2/3     |        2/3         3 _________       |              2/3                 2/3              2/3        |                                                                                               /                       2        \
  |6*|2 + x|        \(-1 + x)            \/ |2 + x|        /   3*x*|2 + x|         6*x*|2 + x|        6*|2 + x|   *(1 + x)|                                                                                 2/3           |3 ________            x         |
x*|------------ + ------------------------------------------ - -------------- - ------------------- + --------------------|            2/3 /     1 + 2*x   1 + 2*x             /  1        1  \\   2*|2 + x|   *(1 + 2*x)*|\/ -1 + x  + -------------------|
  |        2/3                      -1 + x                              5/3             2/3                   2/3         |   x*|2 + x|   *|-2 + ------- + ------- + (1 + 2*x)*|------ + -----||                          |                     2/3        |
  \(-1 + x)                                                     (-1 + x)        (-1 + x)   *(2 + x)   (-1 + x)   *(2 + x) /                \      -1 + x    2 + x              \-1 + x   2 + x//                          \             (-1 + x)   *(2 + x)/
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                                                         3*(-1 + x)                                                                                              5/3                                                               2                        
                                                                                                                                                         (-1 + x)                                                          (-1 + x)                         
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                                                                                                                                 2                                                                                                                          
                                                                                                                          (2 + x)
x(x(2x−13sign⁡(x+2)∣x+2∣3+∣x+2∣23(x−1)23)x−1−6x∣x+2∣23(x−1)23(x+2)−3x∣x+2∣23(x−1)53+6(x+1)∣x+2∣23(x−1)23(x+2)+6∣x+2∣23(x−1)23)3(x−1)+x((2x+1)(1x+2+1x−1)−2+2x+1x+2+2x+1x−1)∣x+2∣23(x−1)53−2(2x+1)(x2(x−1)23(x+2)+x−13)∣x+2∣23(x−1)2(x+2)2\frac{\frac{x \left(\frac{x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{x - 1} - \frac{6 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{3 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{6 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \frac{6 \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{3 \left(x - 1\right)} + \frac{x \left(\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right) - 2 + \frac{2 x + 1}{x + 2} + \frac{2 x + 1}{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} - \frac{2 \left(2 x + 1\right) \left(\frac{x^{2}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \sqrt[3]{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2}}}{\left(x + 2\right)^{2}}
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Tercera derivada [src] 
  /      /        2/3     3 ________            \       /          2/3   3 ________     2                                      3 ________                  \                                                                                               /        2/3     3 ________            \                                       /        2/3     3 ________            \                                                                                                                 \                         /        2/3     3 ________            \                                                                                                                                                                                                                                                                                                                                                                        /                 /        2/3     3 ________            \                                                              \
  |      | |2 + x|      2*\/ -1 + x *sign(2 + x)|       |   |2 + x|      \/ -1 + x *sign (2 + x)        2*sign(2 + x)        6*\/ -1 + x *DiracDelta(2 + x)|                                                                                               | |2 + x|      2*\/ -1 + x *sign(2 + x)|                                       | |2 + x|      2*\/ -1 + x *sign(2 + x)|                                                                                                                 |                         | |2 + x|      2*\/ -1 + x *sign(2 + x)|                                                                                                                                                                                                                                                                                                                                                                        |                 | |2 + x|      2*\/ -1 + x *sign(2 + x)|                                                              |
  |  3*x*|----------- + ------------------------|   2*x*|- ----------- - ----------------------- + ----------------------- + ------------------------------|                                                                                           6*x*|----------- + ------------------------|                             6*(1 + x)*|----------- + ------------------------|                                                                                                                 |                     9*x*|----------- + ------------------------|                                                              /                                                                                                                 /  1        1  \             /  1        1  \                   \                                                                                                                       |               x*|----------- + ------------------------|                                                              |
  |      |        2/3         3 _________       |       |          5/3                 4/3                 2/3 3 _________            3 _________          |               2/3                2/3                2/3                     2/3               |        2/3         3 _________       |                                       |        2/3         3 _________       |                 2/3                   2/3                                                                       |               2/3       |        2/3         3 _________       |                 2/3               2/3                        |                                                                                                       (1 + 2*x)*|------ + -----|   (1 + 2*x)*|------ + -----|                   |                /                       2        \                                                                     |         2/3     |        2/3         3 _________       |              2/3                 2/3              2/3        |
  |      \(-1 + x)            \/ |2 + x|        /       \  (-1 + x)             |2 + x|            (-1 + x)   *\/ |2 + x|             \/ |2 + x|           /   15*x*|2 + x|         18*|2 + x|         72*|2 + x|   *(1 + x)   30*|2 + x|   *(1 + x)       \(-1 + x)            \/ |2 + x|        /       6*x*sign(2 + x)                 \(-1 + x)            \/ |2 + x|        /     30*x*|2 + x|          54*x*|2 + x|                 12*x*sign(2 + x)               12*(1 + x)*sign(2 + x)    |   27*x*|2 + x|          \(-1 + x)            \/ |2 + x|        /     54*x*|2 + x|        54*|2 + x|   *(1 + x)            2/3 |    8        8                 /    1          1              1        \   3*(1 + 2*x)   3*(1 + 2*x)             \-1 + x   2 + x/             \-1 + x   2 + x/     4*(1 + 2*x)   |            2/3 |3 ________            x         | /     1 + 2*x   1 + 2*x             /  1        1  \\               |6*|2 + x|        \(-1 + x)            \/ |2 + x|        /   3*x*|2 + x|         6*x*|2 + x|        6*|2 + x|   *(1 + x)|
x*|- -------------------------------------------- + -------------------------------------------------------------------------------------------------------- + --------------- + ------------------- - --------------------- - --------------------- - -------------------------------------------- - ----------------------- + -------------------------------------------------- + ------------------- + -------------------- - ------------------------------- + -------------------------------| - --------------- + -------------------------------------------- - ------------------- + ---------------------   x*|2 + x|   *|- ------ - ----- + 2*(1 + 2*x)*|--------- + -------- + ----------------| + ----------- + ----------- + -------------------------- + -------------------------- + ----------------|   3*|2 + x|   *|\/ -1 + x  + -------------------|*|-2 + ------- + ------- + (1 + 2*x)*|------ + -----||   x*(1 + 2*x)*|------------ + ------------------------------------------ - -------------- - ------------------- + --------------------|
  |                           2                                                                      -1 + x                                                              8/3             2/3                    2/3        2            5/3                          (-1 + x)*(2 + x)                         5/3 3 _________                    (-1 + x)*(2 + x)                            5/3                   2/3        2           2/3         3 _________           2/3         3 _________|             5/3                        -1 + x                              2/3                    2/3                         |  -1 + x   2 + x               |        2          2   (-1 + x)*(2 + x)|            2             2              -1 + x                       2 + x              (-1 + x)*(2 + x)|                |                     2/3        | \      -1 + x    2 + x              \-1 + x   2 + x//               |        2/3                      -1 + x                              5/3             2/3                   2/3         |
  \                   (-1 + x)                                                                                                                                   (-1 + x)        (-1 + x)   *(2 + x)    (-1 + x)   *(2 + x)     (-1 + x)   *(2 + x)                                                   (-1 + x)   *\/ |2 + x|                                                         (-1 + x)   *(2 + x)   (-1 + x)   *(2 + x)    (-1 + x)   *(2 + x)*\/ |2 + x|    (-1 + x)   *(2 + x)*\/ |2 + x| /     (-1 + x)                                                       (-1 + x)   *(2 + x)    (-1 + x)   *(2 + x)                 \                               \(-1 + x)    (2 + x)                    /    (-1 + x)       (2 + x)                                                                               /                \             (-1 + x)   *(2 + x)/                                                                     \(-1 + x)                                                     (-1 + x)        (-1 + x)   *(2 + x)   (-1 + x)   *(2 + x) /
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                                                                                                                                                                                                                                                                                                     9*(-1 + x)                                                                                                                                                                                                                                                                                                                                                                                                         5/3                                                                                                                                                    2                                                                                                                   2                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                (-1 + x)                                                                                                                                               (-1 + x)                                                                                                            (-1 + x) *(2 + x)                                                          
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               (2 + x)
−x(2x+1)(x(2x−13sign⁡(x+2)∣x+2∣3+∣x+2∣23(x−1)23)x−1−6x∣x+2∣23(x−1)23(x+2)−3x∣x+2∣23(x−1)53+6(x+1)∣x+2∣23(x−1)23(x+2)+6∣x+2∣23(x−1)23)(x−1)2(x+2)−x(2(2x+1)(1(x+2)2+1(x−1)(x+2)+1(x−1)2)+(2x+1)(1x+2+1x−1)x+2−8x+2+3(2x+1)(x+2)2+(2x+1)(1x+2+1x−1)x−1−8x−1+4(2x+1)(x−1)(x+2)+3(2x+1)(x−1)2)∣x+2∣23(x−1)53+x(2x(6x−13δ(x+2)∣x+2∣3−x−13sign⁡2(x+2)∣x+2∣43+2sign⁡(x+2)(x−1)23∣x+2∣3−∣x+2∣23(x−1)53)x−1−6x(2x−13sign⁡(x+2)∣x+2∣3+∣x+2∣23(x−1)23)(x−1)(x+2)−3x(2x−13sign⁡(x+2)∣x+2∣3+∣x+2∣23(x−1)23)(x−1)2−12xsign⁡(x+2)(x−1)23(x+2)∣x+2∣3+54x∣x+2∣23(x−1)23(x+2)2−6xsign⁡(x+2)(x−1)53∣x+2∣3+30x∣x+2∣23(x−1)53(x+2)+15x∣x+2∣23(x−1)83+6(x+1)(2x−13sign⁡(x+2)∣x+2∣3+∣x+2∣23(x−1)23)(x−1)(x+2)+12(x+1)sign⁡(x+2)(x−1)23(x+2)∣x+2∣3−72(x+1)∣x+2∣23(x−1)23(x+2)2+18∣x+2∣23(x−1)23(x+2)−30(x+1)∣x+2∣23(x−1)53(x+2))+9x(2x−13sign⁡(x+2)∣x+2∣3+∣x+2∣23(x−1)23)x−1−54x∣x+2∣23(x−1)23(x+2)−27x∣x+2∣23(x−1)53+54(x+1)∣x+2∣23(x−1)23(x+2)9(x−1)+3(x2(x−1)23(x+2)+x−13)((2x+1)(1x+2+1x−1)−2+2x+1x+2+2x+1x−1)∣x+2∣23(x−1)2(x+2)2\frac{- \frac{x \left(2 x + 1\right) \left(\frac{x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{x - 1} - \frac{6 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{3 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{6 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \frac{6 \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right)^{2} \left(x + 2\right)} - \frac{x \left(2 \left(2 x + 1\right) \left(\frac{1}{\left(x + 2\right)^{2}} + \frac{1}{\left(x - 1\right) \left(x + 2\right)} + \frac{1}{\left(x - 1\right)^{2}}\right) + \frac{\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right)}{x + 2} - \frac{8}{x + 2} + \frac{3 \left(2 x + 1\right)}{\left(x + 2\right)^{2}} + \frac{\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right)}{x - 1} - \frac{8}{x - 1} + \frac{4 \left(2 x + 1\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{3 \left(2 x + 1\right)}{\left(x - 1\right)^{2}}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{x \left(\frac{2 x \left(\frac{6 \sqrt[3]{x - 1} \delta\left(x + 2\right)}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{\sqrt[3]{x - 1} \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left|{x + 2}\right|^{\frac{4}{3}}} + \frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{2}{3}} \sqrt[3]{\left|{x + 2}\right|}} - \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}}\right)}{x - 1} - \frac{6 x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right) \left(x + 2\right)} - \frac{3 x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right)^{2}} - \frac{12 x \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{54 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)^{2}} - \frac{6 x \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{5}{3}} \sqrt[3]{\left|{x + 2}\right|}} + \frac{30 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}} \left(x + 2\right)} + \frac{15 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{8}{3}}} + \frac{6 \left(x + 1\right) \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{12 \left(x + 1\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} - \frac{72 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)^{2}} + \frac{18 \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{30 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}} \left(x + 2\right)}\right) + \frac{9 x \left(\frac{2 \sqrt[3]{x - 1} \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}}}\right)}{x - 1} - \frac{54 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} - \frac{27 x \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{5}{3}}} + \frac{54 \left(x + 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)}}{9 \left(x - 1\right)} + \frac{3 \left(\frac{x^{2}}{\left(x - 1\right)^{\frac{2}{3}} \left(x + 2\right)} + \sqrt[3]{x - 1}\right) \left(\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right) - 2 + \frac{2 x + 1}{x + 2} + \frac{2 x + 1}{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2}}}{\left(x + 2\right)^{2}}
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