First Derivative of the loglogistic4 Model

$$\frac{dy}{dx} = \frac{b\,(d - a)\,r}{x\,(1 + r)^2} \quad\text{where } r = (c/x)^b$$

Usage

dydx_loglogistic4(x, a, b, c, d)

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).

Value

Numeric vector of dy/dx values.

See also

Other derivatives: dydx_gompertz4(), dydx_logistic4(), dydx_logistic5(), dydx_loglogistic5()