# How do you find the derivative of a parametric equation?

## How do you find the derivative of a parametric equation?

The derivative of the parametrically defined curve x=x(t) and y=y(t) can be calculated using the formula dydx=y′(t)x′(t). Using the derivative, we can find the equation of a tangent line to a parametric curve.

## How do you find the initial velocity of a parametric equation?

Projectile motion depends on two parametric equations: x=(v0cosθ)t and y=−16t2+(v0sinθ)t+h. Initial velocity is symbolized as v0. θ represents the initial angle of the object when thrown, and h represents the height at which the object is propelled.

Is dy dx same as dy dt dx dt?

The Chain Rule states that the derivative for the parametric curve is the ratio of to . Symbolically, . Recall that and that dy/dt represents the rate of change of y with respect to t, dx/dt represents the rate of change of x with respect to t, and dy/dx represents the rate of change of y with respect to x.

What is line legend?

LineLegend uses a line with style coli through a marker to identify label lbli with curves and markers in the visualization or other legended item. Legended[expr,LineLegend[…]] can be used to apply a legend to an arbitrary expression expr.

### What is plot in Mathematica?

Plot is known as a function plot or graph of a function. Plot evaluates f at values of x in the domain being plotted over, and connects the points {x,f[x]} to form a curve showing how f varies with x. It visualizes the set . Gaps are left at any x where the fi evaluate to anything other than real numbers or Quantity.

### What is parametric function in calculus?

Summary. A function with a one-dimensional input and a multidimensional output can be thought of as drawing a curve in space. Such a function is called a parametric function, and its input is called a parameter. Sometimes in multivariable calculus, you need to find a parametric function that draws a particular curve.