Implicit And Parametric Functions

Here we will look at functions given implicitly or parametrically, see Implicit and parametric functions in Functions - Theory. When working with implicit or parametric curves, it is often helpful to treat them as graphs of functions. Unfortunately, we not always find an explicit description of the form y = y(x). Fortunately, even without finding this explicit form we can often calculate its derivative y(x), that is, the spatial derivative with respect to x. In the following sections we will explain how it is done.

We will also show how to sketch parametric functions.

• Implicit functions and implicit differentiation.
• Derivative of parametric functions.
• Sketching a parametric function.