First Derivative of the 4PL Model

$$\frac{dy}{dx} = \frac{(d - a)\,u}{b\,(1 + u)^2} \quad\text{where } u = \exp\!\left(-\frac{x - c}{b}\right)$$

Usage

dydx_logistic4(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_logistic5(), dydx_loglogistic4(), dydx_loglogistic5()