First Derivative of the loglogistic5 Model

$$\frac{dy}{dx} = b\,(d - a)\,\exp(-b(x-c))\, u^{-1/g - 1} \quad\text{where } u = 1 + g\,\exp(-b(x-c))$$

Usage

dydx_loglogistic5(x, a, b, c, d, g)

Arguments

x

Numeric vector. Independent variable (typically log10-concentration).

a

Numeric scalar. Lower asymptote (baseline response).

b

Numeric scalar. Scale parameter (\(b > 0\)); controls steepness.

c

Numeric scalar. Inflection-point location on the x-axis.

d

Numeric scalar. Upper asymptote (saturation response).

g

Numeric scalar. Asymmetry (Richards) parameter (\(g > 0\)).

Value

Numeric vector of dy/dx values.

See also

Other derivatives: dydx_gompertz4(), dydx_logistic4(), dydx_logistic5(), dydx_loglogistic4()