Derivada de x^|x-1|

Ha introducido [src]

 |x - 1|
x

$$x^{\left|{x - 1}\right|}$$

x^|x - 1|

Solución detallada

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Perola derivada

$\left(\log{\left(\left|{x - 1}\right| \right)} + 1\right) \left|{x - 1}\right|^{\left|{x - 1}\right|}$
Simplificamos:

$\left(\log{\left(\left|{x - 1}\right| \right)} + 1\right) \left|{x - 1}\right|^{\left|{x - 1}\right|}$

Respuesta:

$\left(\log{\left(\left|{x - 1}\right| \right)} + 1\right) \left|{x - 1}\right|^{\left|{x - 1}\right|}$

Primera derivada [src]

 |x - 1| /|x - 1|                      \
x       *|------- + log(x)*sign(-1 + x)|
         \   x                         /

$$x^{\left|{x - 1}\right|} \left(\log{\left(x \right)} \operatorname{sign}{\left(x - 1 \right)} + \frac{\left|{x - 1}\right|}{x}\right)$$

Simplificar

Segunda derivada [src]

          /                                2                                                          \
 |-1 + x| |/|-1 + x|                      \    |-1 + x|   2*sign(-1 + x)                              |
x        *||-------- + log(x)*sign(-1 + x)|  - -------- + -------------- + 2*DiracDelta(-1 + x)*log(x)|
          |\   x                          /        2            x                                     |
          \                                       x                                                   /

$$x^{\left|{x - 1}\right|} \left(\left(\log{\left(x \right)} \operatorname{sign}{\left(x - 1 \right)} + \frac{\left|{x - 1}\right|}{x}\right)^{2} + 2 \log{\left(x \right)} \delta\left(x - 1\right) + \frac{2 \operatorname{sign}{\left(x - 1 \right)}}{x} - \frac{\left|{x - 1}\right|}{x^{2}}\right)$$

Simplificar

Tercera derivada [src]

          /                                3                                                                                                                                                                                       \
 |-1 + x| |/|-1 + x|                      \    3*sign(-1 + x)   2*|-1 + x|                                      /|-1 + x|                      \ /  |-1 + x|   2*sign(-1 + x)                              \   6*DiracDelta(-1 + x)|
x        *||-------- + log(x)*sign(-1 + x)|  - -------------- + ---------- + 2*DiracDelta(-1 + x, 1)*log(x) + 3*|-------- + log(x)*sign(-1 + x)|*|- -------- + -------------- + 2*DiracDelta(-1 + x)*log(x)| + --------------------|
          |\   x                          /           2              3                                          \   x                          / |      2            x                                     |            x          |
          \                                          x              x                                                                            \     x                                                   /                       /

$$x^{\left|{x - 1}\right|} \left(\left(\log{\left(x \right)} \operatorname{sign}{\left(x - 1 \right)} + \frac{\left|{x - 1}\right|}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \operatorname{sign}{\left(x - 1 \right)} + \frac{\left|{x - 1}\right|}{x}\right) \left(2 \log{\left(x \right)} \delta\left(x - 1\right) + \frac{2 \operatorname{sign}{\left(x - 1 \right)}}{x} - \frac{\left|{x - 1}\right|}{x^{2}}\right) + 2 \log{\left(x \right)} \delta^{\left( 1 \right)}\left( x - 1 \right) + \frac{6 \delta\left(x - 1\right)}{x} - \frac{3 \operatorname{sign}{\left(x - 1 \right)}}{x^{2}} + \frac{2 \left|{x - 1}\right|}{x^{3}}\right)$$

Simplificar

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