Partial Derivatives

Definition

Partial derivatives are derivatives taken with respect to one variable while holding other variables constant. They measure how much a function changes when only one variable changes at a time.

Analogy

Imagine you're baking cookies with multiple ingredients. Taking partial derivatives would be like measuring how much each ingredient affects the taste of the cookies individually, while keeping all other ingredients constant.

Related terms

Total Derivative: A derivative that takes into account changes in all variables simultaneously.

Chain Rule: A rule used to find the derivative of a composite function by multiplying the derivatives of its individual components.

Gradient Vector: A vector that points in the direction of steepest increase of a function and whose magnitude represents the rate of change.