Sr Examen

Otras calculadoras

Derivada de x(x-1)^3+2ln|x-2|-0,2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
         3                    1
x*(x - 1)  + 2*log(|x - 2|) - -
                              5
$$\left(x \left(x - 1\right)^{3} + 2 \log{\left(\left|{x - 2}\right| \right)}\right) - \frac{1}{5}$$
x*(x - 1)^3 + 2*log(|x - 2|) - 1/5
Primera derivada [src]
       3   2*sign(-2 + x)              2
(x - 1)  + -------------- + 3*x*(x - 1) 
              |x - 2|                   
$$3 x \left(x - 1\right)^{2} + \left(x - 1\right)^{3} + \frac{2 \operatorname{sign}{\left(x - 2 \right)}}{\left|{x - 2}\right|}$$
Segunda derivada [src]
  /                  2                                              \
  |          2   sign (-2 + x)   2*DiracDelta(-2 + x)               |
2*|3*(-1 + x)  - ------------- + -------------------- + 3*x*(-1 + x)|
  |                        2           |-2 + x|                     |
  \                (-2 + x)                                         /
$$2 \left(3 x \left(x - 1\right) + 3 \left(x - 1\right)^{2} + \frac{2 \delta\left(x - 2\right)}{\left|{x - 2}\right|} - \frac{\operatorname{sign}^{2}{\left(x - 2 \right)}}{\left(x - 2\right)^{2}}\right)$$
Tercera derivada [src]
  /                  2                                                                      \
  |            2*sign (-2 + x)   2*DiracDelta(-2 + x, 1)   6*DiracDelta(-2 + x)*sign(-2 + x)|
2*|-9 + 12*x + --------------- + ----------------------- - ---------------------------------|
  |                       3              |-2 + x|                              2            |
  \               (-2 + x)                                             (-2 + x)             /
$$2 \left(12 x - 9 + \frac{2 \delta^{\left( 1 \right)}\left( x - 2 \right)}{\left|{x - 2}\right|} - \frac{6 \delta\left(x - 2\right) \operatorname{sign}{\left(x - 2 \right)}}{\left(x - 2\right)^{2}} + \frac{2 \operatorname{sign}^{2}{\left(x - 2 \right)}}{\left(x - 2\right)^{3}}\right)$$