Differentiation of parametric equations

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." Differentiation of this function obtained by using chain rule. Example of parametric equations. Together, these equations are called a parametric equation.

Examples of parametric equations

Derivative of parametric equations

Given the parametric equations and x = f(t), then y = g(t), then

Example
Differentiate the following with respect to x.

2 Key Ideas

1. Notice that we need to rearrange the derivative of x equation x=f(t). See Picture below.
2. Differentiation of parametric equations obtained by using chain rule and the final derivative is in term of t.