- #1
Shaybay92
- 124
- 0
Just a quick question... if we have f(x,y,z) and x(t), y(t), z(t), without substituting in what x y and z are in f, how do we calculate df/dt?
Shaybay92 said:Just a quick question... if we have f(x,y,z) and x(t), y(t), z(t), without substituting in what x y and z are in f, how do we calculate df/dt?
Shaybay92 said:Where did this come from? I can't see why we should add the contributions of each?
Parametric equations are a set of equations that express the coordinates of a point in terms of one or more independent variables, usually denoted by t. These equations are commonly used to represent curves or surfaces in mathematics and physics.
To find the derivative of a parametric equation, you can use the chain rule. First, take the derivative of each individual equation with respect to the independent variable t. Then, substitute these derivatives into the formula for the chain rule: dy/dx = (dy/dt) / (dx/dt).
A parametric equation describes a curve or surface in terms of one or more independent variables, while a Cartesian equation describes the same curve or surface in terms of x and y coordinates. Parametric equations are often used when working with more complex curves, while Cartesian equations are more commonly used for simpler curves.
Yes, parametric equations can be used to represent three-dimensional figures by adding a third parameter, usually denoted by z. This allows for the representation of curves and surfaces in three-dimensional space.
Parametric equations are used in many fields, including physics, engineering, and computer graphics. They can be used to model the motion of objects, design complex shapes and curves, and generate computer-generated images and animations.