Explain the difference between regular and partial differentiation.
Regular differentiation is the process of finding the gradient of a function at a given point. It involves taking the derivative of the function with respect to each independent variable at the point. Partial differentiation is a form of differentiation which is used to find the partial derivatives of a function with respect to one or more independent variables at a given point. It involves taking the limit of the derivative of the function with respect to a particular independent variable as the other variables are kept constant. The resulting quantity is called the partial derivative of the function with respect to the specified variable.
Regular differentiation is the process of calculating the rate of change of a scalar field at a single point, while partial differentiation is the process of calculating the rate of change of a scalar field at multiple points. Regular differentiation simply requires differentiating a single function, while partial differentiation requires differentiating multiple functions that could depend on multiple variables.