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Derivada de la función/ y=(((x-2)^4)^(1/3))/((x-5)(x+1)^7)

Derivada de y=(((x-2)^4)^(1/3))/((x-5)(x+1)^7)

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

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Solución

Ha introducido [src] 
    __________  
 3 /        4   
 \/  (x - 2)    
----------------
               7
(x - 5)*(x + 1)
(x−2)43(x−5)(x+1)7\frac{\sqrt[3]{\left(x - 2\right)^{4}}}{\left(x - 5\right) \left(x + 1\right)^{7}} 
((x - 2)^4)^(1/3)/(((x - 5)*(x + 1)^7))
Primera derivada [src] 
         4/3        1                                                       
4*|x - 2|   *----------------                                               
                    7                  4/3 /         7            6        \
             (x + 1) *(x - 5)   |x - 2|   *\- (x + 1)  - 7*(x + 1) *(x - 5)/
----------------------------- + --------------------------------------------
          3*(x - 2)                                 14        2             
                                             (x + 1)  *(x - 5)
41(x−5)(x+1)7∣x−2∣433(x−2)+(−7(x−5)(x+1)6−(x+1)7)∣x−2∣43(x−5)2(x+1)14\frac{4 \frac{1}{\left(x - 5\right) \left(x + 1\right)^{7}} \left|{x - 2}\right|^{\frac{4}{3}}}{3 \left(x - 2\right)} + \frac{\left(- 7 \left(x - 5\right) \left(x + 1\right)^{6} - \left(x + 1\right)^{7}\right) \left|{x - 2}\right|^{\frac{4}{3}}}{\left(x - 5\right)^{2} \left(x + 1\right)^{14}}
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Segunda derivada [src] 
               /  /                 3*|-2 + x|\   /-17 + 4*x               /  1        7  \   14*(-7 + 2*x)   7*(-17 + 4*x)\                                       \
               |2*|4*sign(-2 + x) - ----------|   |--------- + (-17 + 4*x)*|------ + -----| - ------------- + -------------|*|-2 + x|                              |
  3 __________ |  \                   -2 + x  /   \  -5 + x                \-5 + x   1 + x/       1 + x           1 + x    /               8*(-17 + 4*x)*|-2 + x|  |
2*\/ |-2 + x| *|------------------------------- + ----------------------------------------------------------------------------------- - ---------------------------|
               \           9*(-2 + x)                                               (1 + x)*(-5 + x)                                    3*(1 + x)*(-5 + x)*(-2 + x)/
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                                                                                7                                                                                   
                                                                         (1 + x) *(-5 + x)
2(2(4sign⁡(x−2)−3∣x−2∣x−2)9(x−2)+((4x−17)(7x+1+1x−5)−14(2x−7)x+1+7(4x−17)x+1+4x−17x−5)∣x−2∣(x−5)(x+1)−8(4x−17)∣x−2∣3(x−5)(x−2)(x+1))∣x−2∣3(x−5)(x+1)7\frac{2 \left(\frac{2 \left(4 \operatorname{sign}{\left(x - 2 \right)} - \frac{3 \left|{x - 2}\right|}{x - 2}\right)}{9 \left(x - 2\right)} + \frac{\left(\left(4 x - 17\right) \left(\frac{7}{x + 1} + \frac{1}{x - 5}\right) - \frac{14 \left(2 x - 7\right)}{x + 1} + \frac{7 \left(4 x - 17\right)}{x + 1} + \frac{4 x - 17}{x - 5}\right) \left|{x - 2}\right|}{\left(x - 5\right) \left(x + 1\right)} - \frac{8 \left(4 x - 17\right) \left|{x - 2}\right|}{3 \left(x - 5\right) \left(x - 2\right) \left(x + 1\right)}\right) \sqrt[3]{\left|{x - 2}\right|}}{\left(x - 5\right) \left(x + 1\right)^{7}}
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Tercera derivada [src] 
  /                                                                                                                      /                                                                                                                                            /  1        7  \                                    /  1        7  \                 /  1        7  \                   \                                                                                                                                                      \
  |  /      2                     4/3                                           3 __________             \               |                                                                                                                                (-17 + 4*x)*|------ + -----|                      14*(-7 + 2*x)*|------ + -----|   7*(-17 + 4*x)*|------ + -----|                   |                                                                                                                                                      |
  |  |2*sign (-2 + x)   9*|-2 + x|         3 __________                      12*\/ |-2 + x| *sign(-2 + x)|           4/3 |  294*(-7 + 2*x)                 /    1          28             7        \   3*(-17 + 4*x)   42*(-11 + 4*x)   105*(-17 + 4*x)               \-5 + x   1 + x/    42*(-7 + 2*x)                   \-5 + x   1 + x/                 \-5 + x   1 + x/    28*(-17 + 4*x) |                                                                                                                                                      |
  |4*|--------------- + ------------- + 12*\/ |-2 + x| *DiracDelta(-2 + x) - ----------------------------|   |-2 + x|   *|- -------------- + 2*(-17 + 4*x)*|--------- + -------- + ----------------| + ------------- + -------------- + --------------- + ---------------------------- - ---------------- - ------------------------------ + ------------------------------ + ----------------|             4/3 /-17 + 4*x               /  1        7  \   14*(-7 + 2*x)   7*(-17 + 4*x)\     3 __________             /                 3*|-2 + x|\|
  |  |          2/3               2                                                     -2 + x           |               |            2                    |        2          2   (1 + x)*(-5 + x)|             2               2                 2                 -5 + x              (1 + x)*(-5 + x)               1 + x                            1 + x                (1 + x)*(-5 + x)|   4*|-2 + x|   *|--------- + (-17 + 4*x)*|------ + -----| - ------------- + -------------|   4*\/ |-2 + x| *(-17 + 4*x)*|4*sign(-2 + x) - ----------||
  |  \  |-2 + x|          (-2 + x)                                                                       /               \     (1 + x)                     \(-5 + x)    (1 + x)                    /     (-5 + x)         (1 + x)           (1 + x)                                                                                                                                           /                 \  -5 + x                \-5 + x   1 + x/       1 + x           1 + x    /                              \                   -2 + x  /|
2*|------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- - --------------------------------------------------------|
  \                                              27*(-2 + x)                                                                                                                                                                                  (1 + x)*(-5 + x)                                                                                                                                                                   (1 + x)*(-5 + x)*(-2 + x)                                                 3*(1 + x)*(-5 + x)*(-2 + x)               /
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                                                                                                                                                                                                                                                                         7                                                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                  (1 + x) *(-5 + x)
2(4(12∣x−2∣3δ(x−2)+2sign⁡2(x−2)∣x−2∣23−12∣x−2∣3sign⁡(x−2)x−2+9∣x−2∣43(x−2)2)27(x−2)−(2(4x−17)(28(x+1)2+7(x−5)(x+1)+1(x−5)2)−14(2x−7)(7x+1+1x−5)x+1+7(4x−17)(7x+1+1x−5)x+1−294(2x−7)(x+1)2+105(4x−17)(x+1)2+42(4x−11)(x+1)2+(4x−17)(7x+1+1x−5)x−5−42(2x−7)(x−5)(x+1)+28(4x−17)(x−5)(x+1)+3(4x−17)(x−5)2)∣x−2∣43(x−5)(x+1)−4(4x−17)(4sign⁡(x−2)−3∣x−2∣x−2)∣x−2∣33(x−5)(x−2)(x+1)+4((4x−17)(7x+1+1x−5)−14(2x−7)x+1+7(4x−17)x+1+4x−17x−5)∣x−2∣43(x−5)(x−2)(x+1))(x−5)(x+1)7\frac{2 \left(\frac{4 \left(12 \sqrt[3]{\left|{x - 2}\right|} \delta\left(x - 2\right) + \frac{2 \operatorname{sign}^{2}{\left(x - 2 \right)}}{\left|{x - 2}\right|^{\frac{2}{3}}} - \frac{12 \sqrt[3]{\left|{x - 2}\right|} \operatorname{sign}{\left(x - 2 \right)}}{x - 2} + \frac{9 \left|{x - 2}\right|^{\frac{4}{3}}}{\left(x - 2\right)^{2}}\right)}{27 \left(x - 2\right)} - \frac{\left(2 \left(4 x - 17\right) \left(\frac{28}{\left(x + 1\right)^{2}} + \frac{7}{\left(x - 5\right) \left(x + 1\right)} + \frac{1}{\left(x - 5\right)^{2}}\right) - \frac{14 \left(2 x - 7\right) \left(\frac{7}{x + 1} + \frac{1}{x - 5}\right)}{x + 1} + \frac{7 \left(4 x - 17\right) \left(\frac{7}{x + 1} + \frac{1}{x - 5}\right)}{x + 1} - \frac{294 \left(2 x - 7\right)}{\left(x + 1\right)^{2}} + \frac{105 \left(4 x - 17\right)}{\left(x + 1\right)^{2}} + \frac{42 \left(4 x - 11\right)}{\left(x + 1\right)^{2}} + \frac{\left(4 x - 17\right) \left(\frac{7}{x + 1} + \frac{1}{x - 5}\right)}{x - 5} - \frac{42 \left(2 x - 7\right)}{\left(x - 5\right) \left(x + 1\right)} + \frac{28 \left(4 x - 17\right)}{\left(x - 5\right) \left(x + 1\right)} + \frac{3 \left(4 x - 17\right)}{\left(x - 5\right)^{2}}\right) \left|{x - 2}\right|^{\frac{4}{3}}}{\left(x - 5\right) \left(x + 1\right)} - \frac{4 \left(4 x - 17\right) \left(4 \operatorname{sign}{\left(x - 2 \right)} - \frac{3 \left|{x - 2}\right|}{x - 2}\right) \sqrt[3]{\left|{x - 2}\right|}}{3 \left(x - 5\right) \left(x - 2\right) \left(x + 1\right)} + \frac{4 \left(\left(4 x - 17\right) \left(\frac{7}{x + 1} + \frac{1}{x - 5}\right) - \frac{14 \left(2 x - 7\right)}{x + 1} + \frac{7 \left(4 x - 17\right)}{x + 1} + \frac{4 x - 17}{x - 5}\right) \left|{x - 2}\right|^{\frac{4}{3}}}{\left(x - 5\right) \left(x - 2\right) \left(x + 1\right)}\right)}{\left(x - 5\right) \left(x + 1\right)^{7}}
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