Partial derivatives measure how a multivariable function changes when one input varies and the others are held constant. This complete Calculus 3 lesson develops limit definitions, trace curves, first and mixed partials, tangent planes, the multivariable chain rule, linear approximation, rigorous counterexamples, and solved practice problems.
Which direction makes a multivariable function increase fastest? Learn how the gradient packages partial derivatives, how to calculate directional derivatives with unit vectors and dot products, and why gradients cross level curves at right angles.
