This document discusses the total derivative and methods for finding derivatives of functions with multiple variables. The total derivative expresses the total differential of a function u with respect to time t as the sum of the partial derivatives of u with respect to each variable x1, x2,...xn, multiplied by the rate of change of that variable with respect to time. The chain rule is used to take derivatives of composite functions, where the output of one function is an input to another. The derivative is expressed as the product of the partial derivatives of each nested function. Derivatives can also be taken for implicit functions, where not all variables can be solved for explicitly. The derivative of one variable with respect to another in an