(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to follow my text book on an application of the chain rule.

Two objects are traveling in elliptical paths given by the following parametric equation.

x1 = 4 cos t

x2 = 2 sin 2t

y1 = 2 sin t

y2 = 3 cos 2t

At what rate is the distance between the two objects changing when t = pi?

2. Relevant equations

distance S = √(x2 - x1)2 + (y2 - y1)2

3. The attempt at a solution

When t = pi

x1 = -4

y1 = 0

x2 = 0

y2 = 3

When t = pi the partial derivatives of s are as follows.

∂s/∂x1 = -(x2 - x1)/√(x2 - x1)2 + (y2 - y1)2 = -1/5(0 + 4) = -4/5

How come we're all of a sudden dividing -(x2 - x1) by S? I guess I'm not grasping the concept of the partial derivative of S with respect to x1 when x1 is an equation either. Would someone be able to elaborate on that? If you need me to explain more, please let me know.

Thanks in advance for any help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Chain Rule For Function of Severable Variables

**Physics Forums | Science Articles, Homework Help, Discussion**