Partial derivatives are classified into two types: First-order partial derivatives are a multivariable function's partial derivatives with respect to each of its variables. There are n first-order partial derivatives for a function with n variables. Higher-order partial derivatives: These are created by taking partial derivatives of a function one after the other. For example, the partial derivative of the first-order partial derivative with regard to the same variable is the second-order partial derivative. This procedure can be repeated to get third-order, fourth-order, and higher-order partial derivatives. In summary, partial derivatives are categorised depending on their order, with the two primary categories being first-order partial derivatives and higher-order partial derivatives.