# 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.