## What do you call Uncle Rates & his nephew? Related Rates!

Related rates problems are one of the culminating techniques of Year 12 mathematical methods. That means that it is a mathematical problem that involves using most of the skills you have developed in calculus so far.

But there is no need to be scared; related rates are merely an application of the chain rule.

In this you can see that there is a relationship between dy/dx and du/dx. That relationship is the factor of dy/du.

In other words, if we want to calculate a value of dy/dx, and we know du/dx, we need to find dy/du.

This can be somewhat challenging, and may require an application of the chain rule in order to do it! I advise using implicit differentiation to help you solve these type of problems – it makes it easier if you can understand it.

If you haven’t studied specialist mathematics (and even if you have!), Implicit differentiation may seem difficult. I’ve found a few interesting resources which may help you get your head around the technique:

And here it is applied to a related rates problem:

Here are some good notes that may help: Paul’s Calculus Notes.

And last, here are some problems worked and solved that use the implicit differentiation technique: Related Rates Problems

ps. Here is the Chapter 11 Checklist

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### 5 Comments on “What do you call Uncle Rates & his nephew? Related Rates!”

1. Patrick Says:

*sigh*
Soo much for not using specialist maths in methods
Would this be a valid technique in the exam?

• CyberChalky Says:

I would use it as a last resort; if it were obvious that using a MM technique would take an excessive amount of effort for marks present.

If I made that decision, I would still be prepared to losing a “workings” mark.

It’s a trade off – you will have to make your own decision.

2. Locky Says:

Okay, I think I actually understand implicit now.

It’s differentiating each with respect to time, needing to know the relationship between the rates, not the values themselves.

And then you differentiate each variable with respect to time, so you end up with a statement involving two different rates. After that, you just sub in the pronumerals and the rate you have and you determine the rate you didn’t have by… Establishing the relationship between the rates with respect to time?

Anyway, I’ve done two examples using it and have gotten correct answers, which is pretty excellent.