se volete farvi delle implementazioni/esperimenti/farvi venire un po' di mal di testa, vi posto un po' di codice
1) codice python della logistica asimmetrica
LL + (-LL + LU)*(exp((S*(Ix - x)/(-LL + LU) + c*(exp(c) + 1)**((-exp(c) - 1)*exp(-c)))*(exp(c) + 1)**((exp(c) + 1)*exp(-c))) + 1)**(-exp(-c))
2) codice python della derivata della logistica asimmetrica
S*(exp(c) + 1)**((exp(c) + 1)*exp(-c))*(exp((S*(Ix - x)/(-LL + LU) + c*(exp(c) + 1)**((-exp(c) - 1)*exp(-c)))*(exp(c) + 1)**((exp(c) + 1)*exp(-c))) + 1)**(-exp(-c))*exp(-c)*exp((S*(Ix - x)/(-LL + LU) + c*(exp(c) + 1)**((-exp(c) - 1)*exp(-c)))*(exp(c) + 1)**((exp(c) + 1)*exp(-c)))/(exp((S*(Ix - x)/(-LL + LU) + c*(exp(c) + 1)**((-exp(c) - 1)*exp(-c)))*(exp(c) + 1)**((exp(c) + 1)*exp(-c))) + 1)
3) Codice LaTeX della derivata
\frac{S \left(e^{c} + 1\right)^{\left(e^{c} + 1\right) e^{- c}} \left(e^{\left(\frac{S \left(Ix - x\right)}{- LL + LU} + c \left(e^{c} + 1\right)^{\left(- e^{c} - 1\right) e^{- c}}\right) \left(e^{c} + 1\right)^{\left(e^{c} + 1\right) e^{- c}}} + 1\right)^{- e^{- c}} e^{- c} e^{\left(\frac{S \left(Ix - x\right)}{- LL + LU} + c \left(e^{c} + 1\right)^{\left(- e^{c} - 1\right) e^{- c}}\right) \left(e^{c} + 1\right)^{\left(e^{c} + 1\right) e^{- c}}}}{e^{\left(\frac{S \left(Ix - x\right)}{- LL + LU} + c \left(e^{c} + 1\right)^{\left(- e^{c} - 1\right) e^{- c}}\right) \left(e^{c} + 1\right)^{\left(e^{c} + 1\right) e^{- c}}} + 1}
