dxdt

dXdt is a shorthand used in plain text for the derivative of a quantity X with respect to time t, commonly written in proper notation as dX/dt. It expresses the instantaneous rate at which X changes as time advances. If X is a function of t, X = X(t), then dX/dt measures how X changes per unit change in t. For example, if X(t) = t^2, then dX/dt = 2t; at t = 3 the rate of change is 6.

When X is a vector-valued function X(t) = [x1(t), x2(t), ...], the derivative dX/dt is the vector of the component derivatives [dx1/dt, dx2/dt, ...]. In physics, the time derivative of a position vector is velocity, and the dot notation Ẋ is widely used to denote dX/dt, especially in mechanics.

In more complex models, X may depend on several variables that themselves depend on time, so the total derivative dX/dt applies and is related by the chain rule. If X depends on t explicitly and also through other variables y(t), then dX/dt combines these dependencies. In contrast, the partial derivative ∂X/∂t holds X fixed with respect to other variables and reflects explicit time dependence only.

Notational notes: dX/dt is standard in calculus, while dXdt appears in informal or plain-text contexts where the division slash is omitted. The concept underpins many fields, including differential equations, dynamical systems, and kinematics. See also derivative, rate of change, velocity, acceleration, chain rule, and multivariable calculus.