Almost there! Just a few clicks from the resource you need.
You can either checkout with the notes in your basket now, or find more notes. The choice is yours!
My Basket
Differentiation in Calculus
Total differentiation in calculus refers to the process of finding the rate of change of a function with respect to multiple variables. It extends the concept of differentiation to functions of more than one variable, allowing us to compute how a function changes when all of its independent variables change simultaneously. If a function depends on variables, the total derivative of with respect to one variable can be computed by considering the contributions of all independent variables. The total differential is represented as: df = \frac{\partial f}{\partial x_1} dx_1 + \frac{\partial f}{\partial x_2} dx_2 + ... + \frac{\partial f}{\partial x_n} dx_n Here, represents the partial derivative of with respect to , and denotes an infinitesimal change in the variable . The total differential gives the best linear approximation to the change in due to small changes in each of the variables. In practical terms, total differentiation is used when variables are interdependent, such as in multivariable optimization problems, and helps understand how changes in one or more variables impact the overall function.
£0.50 Preview Remove