Sr Examen

Otras calculadoras

Derivada de la función/ (x-1)/ |x|^(π)/ |x|^(π)(x-1)

Derivada de |x|^(π)(x-1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   pi        
|x|  *(x - 1)
$$\left(x - 1\right) \left|{x}\right|^{\pi}$$ 
|x|^pi*(x - 1)
Primera derivada [src] 
              pi                
   pi   pi*|x|  *(x - 1)*sign(x)
|x|   + ------------------------
                  |x|
$$\frac{\pi \left(x - 1\right) \left|{x}\right|^{\pi} \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \left|{x}\right|^{\pi}$$
Simplificar
Segunda derivada [src] 
         /         /      2                               2   \            \
      pi |         |  sign (x)   2*DiracDelta(x)   pi*sign (x)|   2*sign(x)|
pi*|x|  *|(-1 + x)*|- -------- + --------------- + -----------| + ---------|
         |         |      2            |x|               2    |      |x|   |
         \         \     x                              x     /            /
$$\pi \left(\left(x - 1\right) \left(\frac{2 \delta\left(x\right)}{\left|{x}\right|} - \frac{\operatorname{sign}^{2}{\left(x \right)}}{x^{2}} + \frac{\pi \operatorname{sign}^{2}{\left(x \right)}}{x^{2}}\right) + \frac{2 \operatorname{sign}{\left(x \right)}}{\left|{x}\right|}\right) \left|{x}\right|^{\pi}$$
Simplificar
Tercera derivada [src] 
         /         /      2                                                              2        2     3             3                                \         2                                 2   \
      pi |         |2*sign (x)   2*DiracDelta(x, 1)   6*DiracDelta(x)*sign(x)   2*pi*sign (x)   pi *sign (x)   pi*sign (x)   6*pi*DiracDelta(x)*sign(x)|   3*sign (x)   6*DiracDelta(x)   3*pi*sign (x)|
pi*|x|  *|(-1 + x)*|---------- + ------------------ - ----------------------- - ------------- + ------------ - ----------- + --------------------------| - ---------- + --------------- + -------------|
         |         |     3              |x|                       2                    3            2              2                      2            |        2             |x|                2     |
         \         \    x                                        x                    x            x *|x|         x *|x|                 x             /       x                                x      /
$$\pi \left(\left(x - 1\right) \left(\frac{2 \delta^{\left( 1 \right)}\left( x \right)}{\left|{x}\right|} - \frac{6 \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{6 \pi \delta\left(x\right) \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{\pi \operatorname{sign}^{3}{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\pi^{2} \operatorname{sign}^{3}{\left(x \right)}}{x^{2} \left|{x}\right|} - \frac{2 \pi \operatorname{sign}^{2}{\left(x \right)}}{x^{3}} + \frac{2 \operatorname{sign}^{2}{\left(x \right)}}{x^{3}}\right) + \frac{6 \delta\left(x\right)}{\left|{x}\right|} - \frac{3 \operatorname{sign}^{2}{\left(x \right)}}{x^{2}} + \frac{3 \pi \operatorname{sign}^{2}{\left(x \right)}}{x^{2}}\right) \left|{x}\right|^{\pi}$$
Simplificar
    © Sr Examen