A partial derivative measures how a function changes with respect to one variable while holding other variables constant. It is fundamental in optimization and gradient-based machine learning because models often depend on many variables at once.
A derivative in which all but one of the variables is considered a constant. For example, the partial derivative of f(x, y) with respect to x is the derivative of f considered as a function of x alone (that is, keeping y constant). The partial derivative of f with respect to x focuses only on how x is changing and ignores all other variables in the equation.