MAMC.B.5

MAMC.B.5: explore, find, use, and apply partial differentiation of functions of two independent variables of the form z = f(x, y) and implicit functions of the form f(x, y, z) = 0; approximate the partial derivatives at a point of a function defined by a table of data; find expressions for the first and second partial derivatives of a function; define and apply the total differential to approximate real-world phenomena; represent the partial derivatives of a system of two functions in two variables using the Jacobian; find the partial derivatives of the composition of functions using the general chain rule; apply partial differentiation to problems of optimization, including problems requiring the use of the Lagrange multiplier; investigate the differential, tangent plane, and normal lines