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Derivada de la función/ (x(x-4))/((x+2)(x-4)^2)^(2/3)

Derivada de (x(x-4))/((x+2)(x-4)^2)^(2/3)

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

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Solución

Ha introducido [src] 
      x*(x - 4)      
---------------------
                  2/3
/               2\   
\(x + 2)*(x - 4) /
x(x−4)((x−4)2(x+2))23\frac{x \left(x - 4\right)}{\left(\left(x - 4\right)^{2} \left(x + 2\right)\right)^{\frac{2}{3}}} 
(x*(x - 4))/((x + 2)*(x - 4)^2)^(2/3)
Primera derivada [src] 
                                     /         2                       \
                                     |2*(x - 4)    2*(-8 + 2*x)*(x + 2)|
                                   x*|---------- + --------------------|
          1                          \    3                 3          /
---------------------*(-4 + 2*x) - -------------------------------------
       2/3        4/3                                 5/3        4/3    
(x + 2)   *|x - 4|                     (x - 4)*(x + 2)   *|x - 4|
−x(2(x−4)23+2(x+2)(2x−8)3)(x−4)(x+2)53∣x−4∣43+1(x+2)23∣x−4∣43(2x−4)- \frac{x \left(\frac{2 \left(x - 4\right)^{2}}{3} + \frac{2 \left(x + 2\right) \left(2 x - 8\right)}{3}\right)}{\left(x - 4\right) \left(x + 2\right)^{\frac{5}{3}} \left|{x - 4}\right|^{\frac{4}{3}}} + \frac{1}{\left(x + 2\right)^{\frac{2}{3}} \left|{x - 4}\right|^{\frac{4}{3}}} \left(2 x - 4\right)
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Segunda derivada [src] 
  /      /  6*(-2 + x)       /  1     2*sign(-4 + x)\    3*x     6*x  \                   \
  |    x*|- ---------- + 2*x*|----- + --------------| + ----- + ------|                   |
  |      \    -4 + x         \2 + x      |-4 + x|   /   2 + x   -4 + x/     4*x*(-2 + x)  |
2*|1 + ---------------------------------------------------------------- - ----------------|
  \                               3*(2 + x)                               (-4 + x)*(2 + x)/
-------------------------------------------------------------------------------------------
                                          2/3         4/3                                  
                                   (2 + x)   *|-4 + x|
2(x(2x(2sign⁡(x−4)∣x−4∣+1x+2)+3xx+2+6xx−4−6(x−2)x−4)3(x+2)−4x(x−2)(x−4)(x+2)+1)(x+2)23∣x−4∣43\frac{2 \left(\frac{x \left(2 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right) + \frac{3 x}{x + 2} + \frac{6 x}{x - 4} - \frac{6 \left(x - 2\right)}{x - 4}\right)}{3 \left(x + 2\right)} - \frac{4 x \left(x - 2\right)}{\left(x - 4\right) \left(x + 2\right)} + 1\right)}{\left(x + 2\right)^{\frac{2}{3}} \left|{x - 4}\right|^{\frac{4}{3}}}
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Tercera derivada [src] 
  /             /                                                                                                                                                         /  1     2*sign(-4 + x)\       /  1     2*sign(-4 + x)\       /  1     2*sign(-4 + x)\                                                                                     \                                                                          \
  |             |           /                                          2                           \                                                           6*(-2 + x)*|----- + --------------|   3*x*|----- + --------------|   6*x*|----- + --------------|                                                                                     |                                                                          |
  |             |  9        |   5       12*DiracDelta(-4 + x)   14*sign (-4 + x)    8*sign(-4 + x) |   36*(-2 + x)     12*x        27*x       24*(-2 + x)                 \2 + x      |-4 + x|   /       \2 + x      |-4 + x|   /       \2 + x      |-4 + x|   /         24*x         12*(-2 + x)*sign(-4 + x)   6*x*sign(-4 + x)   12*x*sign(-4 + x)|                                                                          |
  |           x*|------ + x*|-------- - --------------------- + ---------------- + ----------------| - ----------- + -------- + --------- - ---------------- - ----------------------------------- + ---------------------------- + ---------------------------- + ---------------- - ------------------------ + ---------------- + -----------------|            /  6*(-2 + x)       /  1     2*sign(-4 + x)\    3*x     6*x  \|
  |             |-4 + x     |       2          |-4 + x|                    2       (2 + x)*|-4 + x||            2           2           2   (-4 + x)*(2 + x)                  -4 + x                            2 + x                          -4 + x              (-4 + x)*(2 + x)      (-4 + x)*|-4 + x|       (2 + x)*|-4 + x|   (-4 + x)*|-4 + x||   (-2 + x)*|- ---------- + 2*x*|----- + --------------| + ----- + ------||
  |   3*x       \           \(2 + x)                               (-4 + x)                        /    (-4 + x)     (2 + x)    (-4 + x)                                                                                                                                                                                                             /            \    -4 + x         \2 + x      |-4 + x|   /   2 + x   -4 + x/|
4*|- ------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------|
  \  -4 + x                                                                                                                                                                      9                                                                                                                                                                                                        -4 + x                                /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                             5/3         4/3                                                                                                                                                                                                     
                                                                                                                                                                                                      (2 + x)   *|-4 + x|
4(−x(x(−12δ(x−4)∣x−4∣+8sign⁡(x−4)(x+2)∣x−4∣+5(x+2)2+14sign⁡2(x−4)(x−4)2)+3x(2sign⁡(x−4)∣x−4∣+1x+2)x+2+6xsign⁡(x−4)(x+2)∣x−4∣+12x(x+2)2+6x(2sign⁡(x−4)∣x−4∣+1x+2)x−4+12xsign⁡(x−4)(x−4)∣x−4∣+24x(x−4)(x+2)+27x(x−4)2−6(x−2)(2sign⁡(x−4)∣x−4∣+1x+2)x−4−12(x−2)sign⁡(x−4)(x−4)∣x−4∣−24(x−2)(x−4)(x+2)+9x−4−36(x−2)(x−4)2)9−3xx−4+(x−2)(2x(2sign⁡(x−4)∣x−4∣+1x+2)+3xx+2+6xx−4−6(x−2)x−4)x−4)(x+2)53∣x−4∣43\frac{4 \left(- \frac{x \left(x \left(- \frac{12 \delta\left(x - 4\right)}{\left|{x - 4}\right|} + \frac{8 \operatorname{sign}{\left(x - 4 \right)}}{\left(x + 2\right) \left|{x - 4}\right|} + \frac{5}{\left(x + 2\right)^{2}} + \frac{14 \operatorname{sign}^{2}{\left(x - 4 \right)}}{\left(x - 4\right)^{2}}\right) + \frac{3 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right)}{x + 2} + \frac{6 x \operatorname{sign}{\left(x - 4 \right)}}{\left(x + 2\right) \left|{x - 4}\right|} + \frac{12 x}{\left(x + 2\right)^{2}} + \frac{6 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right)}{x - 4} + \frac{12 x \operatorname{sign}{\left(x - 4 \right)}}{\left(x - 4\right) \left|{x - 4}\right|} + \frac{24 x}{\left(x - 4\right) \left(x + 2\right)} + \frac{27 x}{\left(x - 4\right)^{2}} - \frac{6 \left(x - 2\right) \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right)}{x - 4} - \frac{12 \left(x - 2\right) \operatorname{sign}{\left(x - 4 \right)}}{\left(x - 4\right) \left|{x - 4}\right|} - \frac{24 \left(x - 2\right)}{\left(x - 4\right) \left(x + 2\right)} + \frac{9}{x - 4} - \frac{36 \left(x - 2\right)}{\left(x - 4\right)^{2}}\right)}{9} - \frac{3 x}{x - 4} + \frac{\left(x - 2\right) \left(2 x \left(\frac{2 \operatorname{sign}{\left(x - 4 \right)}}{\left|{x - 4}\right|} + \frac{1}{x + 2}\right) + \frac{3 x}{x + 2} + \frac{6 x}{x - 4} - \frac{6 \left(x - 2\right)}{x - 4}\right)}{x - 4}\right)}{\left(x + 2\right)^{\frac{5}{3}} \left|{x - 4}\right|^{\frac{4}{3}}}
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