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y=ln|(x-4)/(x+4)|
Derivada de la función/ (x-4)/ (x+4)/ y=ln|(x-4)/(x+4)|

Derivada de y=ln|(x-4)/(x+4)|

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

Gráfico:

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Solución

Ha introducido [src] 
   /|x - 4|\
log||-----||
   \|x + 4|/
log⁡(∣x−4x+4∣)\log{\left(\left|{\frac{x - 4}{x + 4}}\right| \right)} 
log(Abs((x - 4)/(x + 4)))
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/  1      -4 + x \     /-4 + x\
|----- - --------|*sign|------|
|4 + x          2|     \4 + x /
\        (4 + x) /             
-------------------------------
            |x - 4|            
            |-----|            
            |x + 4|
(−x−4(x+4)2+1x+4)sign⁡(x−4x+4)∣x−4x+4∣\frac{\left(- \frac{x - 4}{\left(x + 4\right)^{2}} + \frac{1}{x + 4}\right) \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)}}{\left|{\frac{x - 4}{x + 4}}\right|}
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Segunda derivada [src] 
              /                           /-4 + x\       2/-4 + x\ /     -4 + x\\
              |                     2*sign|------|   sign |------|*|-1 + ------||
/     -4 + x\ |  d /    /-4 + x\\         \4 + x /        \4 + x / \     4 + x /|
|-1 + ------|*|- --|sign|------|| + -------------- - ---------------------------|
\     4 + x / |  dx\    \4 + x //       4 + x                      |-4 + x|     |
              |                                            (4 + x)*|------|     |
              \                                                    |4 + x |     /
---------------------------------------------------------------------------------
                                         |-4 + x|                                
                                 (4 + x)*|------|                                
                                         |4 + x |
(x−4x+4−1)(−ddxsign⁡(x−4x+4)−(x−4x+4−1)sign⁡2(x−4x+4)(x+4)∣x−4x+4∣+2sign⁡(x−4x+4)x+4)(x+4)∣x−4x+4∣\frac{\left(\frac{x - 4}{x + 4} - 1\right) \left(- \frac{d}{d x} \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)} - \frac{\left(\frac{x - 4}{x + 4} - 1\right) \operatorname{sign}^{2}{\left(\frac{x - 4}{x + 4} \right)}}{\left(x + 4\right) \left|{\frac{x - 4}{x + 4}}\right|} + \frac{2 \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)}}{x + 4}\right)}{\left(x + 4\right) \left|{\frac{x - 4}{x + 4}}\right|}
Simplificar
Tercera derivada [src] 
              /                                                                           2                                                                                              \
              |                            /-4 + x\     d /    /-4 + x\\     /     -4 + x\      3/-4 + x\         2/-4 + x\ /     -4 + x\     /     -4 + x\ d /    /-4 + x\\     /-4 + x\|
              |    2                 6*sign|------|   4*--|sign|------||   2*|-1 + ------| *sign |------|   6*sign |------|*|-1 + ------|   3*|-1 + ------|*--|sign|------||*sign|------||
/     -4 + x\ |   d /    /-4 + x\\         \4 + x /     dx\    \4 + x //     \     4 + x /       \4 + x /          \4 + x / \     4 + x /     \     4 + x / dx\    \4 + x //     \4 + x /|
|-1 + ------|*|- ---|sign|------|| - -------------- + ------------------ - ------------------------------ + ----------------------------- - ---------------------------------------------|
\     4 + x / |    2\    \4 + x //             2            4 + x                                 2                      2 |-4 + x|                                |-4 + x|              |
              |  dx                     (4 + x)                                         2 |-4 + x|                (4 + x) *|------|                        (4 + x)*|------|              |
              |                                                                  (4 + x) *|------|                         |4 + x |                                |4 + x |              |
              \                                                                           |4 + x |                                                                                       /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                             |-4 + x|                                                                                     
                                                                                     (4 + x)*|------|                                                                                     
                                                                                             |4 + x |
(x−4x+4−1)(−d2dx2sign⁡(x−4x+4)−3(x−4x+4−1)sign⁡(x−4x+4)ddxsign⁡(x−4x+4)(x+4)∣x−4x+4∣+4ddxsign⁡(x−4x+4)x+4−2(x−4x+4−1)2sign⁡3(x−4x+4)(x+4)2∣x−4x+4∣2+6(x−4x+4−1)sign⁡2(x−4x+4)(x+4)2∣x−4x+4∣−6sign⁡(x−4x+4)(x+4)2)(x+4)∣x−4x+4∣\frac{\left(\frac{x - 4}{x + 4} - 1\right) \left(- \frac{d^{2}}{d x^{2}} \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)} - \frac{3 \left(\frac{x - 4}{x + 4} - 1\right) \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)} \frac{d}{d x} \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)}}{\left(x + 4\right) \left|{\frac{x - 4}{x + 4}}\right|} + \frac{4 \frac{d}{d x} \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)}}{x + 4} - \frac{2 \left(\frac{x - 4}{x + 4} - 1\right)^{2} \operatorname{sign}^{3}{\left(\frac{x - 4}{x + 4} \right)}}{\left(x + 4\right)^{2} \left|{\frac{x - 4}{x + 4}}\right|^{2}} + \frac{6 \left(\frac{x - 4}{x + 4} - 1\right) \operatorname{sign}^{2}{\left(\frac{x - 4}{x + 4} \right)}}{\left(x + 4\right)^{2} \left|{\frac{x - 4}{x + 4}}\right|} - \frac{6 \operatorname{sign}{\left(\frac{x - 4}{x + 4} \right)}}{\left(x + 4\right)^{2}}\right)}{\left(x + 4\right) \left|{\frac{x - 4}{x + 4}}\right|}
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Gráfico
Derivada de y=ln|(x-4)/(x+4)|
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