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|x|*(ln(|x|))^(6/7)
Derivada de la función/ (|x|)/ |x|*(ln(|x|))^(6/7)

Derivada de |x|*(ln(|x|))^(6/7)

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

Gráfico:

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Solución

Ha introducido [src] 
       6/7     
|x|*log   (|x|)
log⁡(∣x∣)67∣x∣\log{\left(\left|{x}\right| \right)}^{\frac{6}{7}} \left|{x}\right| 
|x|*log(|x|)^(6/7)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   6/7                  6*sign(x)   
log   (|x|)*sign(x) + --------------
                        7 __________
                      7*\/ log(|x|)
log⁡(∣x∣)67sign⁡(x)+6sign⁡(x)7log⁡(∣x∣)7\log{\left(\left|{x}\right| \right)}^{\frac{6}{7}} \operatorname{sign}{\left(x \right)} + \frac{6 \operatorname{sign}{\left(x \right)}}{7 \sqrt[7]{\log{\left(\left|{x}\right| \right)}}}
Simplificar
Segunda derivada [src] 
  /                              /                           2            2    \                         \
  |                              |  14*DiracDelta(x)   7*sign (x)     sign (x) |                         |
  |                            3*|- ---------------- + ---------- + -----------|*|x|                     |
  |                              |        |x|               2        2         |                 2       |
  |   6/7                        \                         x        x *log(|x|)/           6*sign (x)    |
2*|log   (|x|)*DiracDelta(x) - ----------------------------------------------------- + ------------------|
  |                                                  7 __________                            7 __________|
  \                                               49*\/ log(|x|)                       7*|x|*\/ log(|x|) /
2(−3(−14δ(x)∣x∣+7sign⁡2(x)x2+sign⁡2(x)x2log⁡(∣x∣))∣x∣49log⁡(∣x∣)7+log⁡(∣x∣)67δ(x)+6sign⁡2(x)7log⁡(∣x∣)7∣x∣)2 \left(- \frac{3 \left(- \frac{14 \delta\left(x\right)}{\left|{x}\right|} + \frac{7 \operatorname{sign}^{2}{\left(x \right)}}{x^{2}} + \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}}\right) \left|{x}\right|}{49 \sqrt[7]{\log{\left(\left|{x}\right| \right)}}} + \log{\left(\left|{x}\right| \right)}^{\frac{6}{7}} \delta\left(x\right) + \frac{6 \operatorname{sign}^{2}{\left(x \right)}}{7 \sqrt[7]{\log{\left(\left|{x}\right| \right)}} \left|{x}\right|}\right)
Simplificar
Tercera derivada [src] 
  /                                 /                           2            2    \             /       2                                                               2                                          3                 3      \                               \
  |                                 |  14*DiracDelta(x)   7*sign (x)     sign (x) |             |98*sign (x)   98*DiracDelta(x, 1)   294*DiracDelta(x)*sign(x)   14*sign (x)   42*DiracDelta(x)*sign(x)      7*sign (x)        8*sign (x)   |                               |
  |                               9*|- ---------------- + ---------- + -----------|*sign(x)   3*|----------- + ------------------- - ------------------------- + ----------- - ------------------------ + --------------- + ----------------|*|x|                           |
  |                                 |        |x|               2        2         |             |      3               |x|                        2               3                   2                    2                 2        2     |                               |
  |   6/7                           \                         x        x *log(|x|)/             \     x                                          x               x *log(|x|)         x *log(|x|)          x *|x|*log(|x|)   x *|x|*log (|x|)/       18*DiracDelta(x)*sign(x)|
2*|log   (|x|)*DiracDelta(x, 1) - --------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------|
  |                                                       7 __________                                                                                              7 __________                                                                             7 __________   |
  \                                                    49*\/ log(|x|)                                                                                           343*\/ log(|x|)                                                                        7*|x|*\/ log(|x|)    /
2(−9(−14δ(x)∣x∣+7sign⁡2(x)x2+sign⁡2(x)x2log⁡(∣x∣))sign⁡(x)49log⁡(∣x∣)7+3(98δ(1)(x)∣x∣−294δ(x)sign⁡(x)x2−42δ(x)sign⁡(x)x2log⁡(∣x∣)+7sign⁡3(x)x2log⁡(∣x∣)∣x∣+8sign⁡3(x)x2log⁡(∣x∣)2∣x∣+98sign⁡2(x)x3+14sign⁡2(x)x3log⁡(∣x∣))∣x∣343log⁡(∣x∣)7+log⁡(∣x∣)67δ(1)(x)+18δ(x)sign⁡(x)7log⁡(∣x∣)7∣x∣)2 \left(- \frac{9 \left(- \frac{14 \delta\left(x\right)}{\left|{x}\right|} + \frac{7 \operatorname{sign}^{2}{\left(x \right)}}{x^{2}} + \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}}\right) \operatorname{sign}{\left(x \right)}}{49 \sqrt[7]{\log{\left(\left|{x}\right| \right)}}} + \frac{3 \left(\frac{98 \delta^{\left( 1 \right)}\left( x \right)}{\left|{x}\right|} - \frac{294 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{42 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}} + \frac{7 \operatorname{sign}^{3}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)} \left|{x}\right|} + \frac{8 \operatorname{sign}^{3}{\left(x \right)}}{x^{2} \log{\left(\left|{x}\right| \right)}^{2} \left|{x}\right|} + \frac{98 \operatorname{sign}^{2}{\left(x \right)}}{x^{3}} + \frac{14 \operatorname{sign}^{2}{\left(x \right)}}{x^{3} \log{\left(\left|{x}\right| \right)}}\right) \left|{x}\right|}{343 \sqrt[7]{\log{\left(\left|{x}\right| \right)}}} + \log{\left(\left|{x}\right| \right)}^{\frac{6}{7}} \delta^{\left( 1 \right)}\left( x \right) + \frac{18 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{7 \sqrt[7]{\log{\left(\left|{x}\right| \right)}} \left|{x}\right|}\right)
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Gráfico
Derivada de |x|*(ln(|x|))^(6/7)
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