Chain Rule

  2. Calculus
  3. Chain Rule
    4. 30'

The Chain Rule is used for differentiating composite functions. The rule itself looks really quite simple (and it is not too difficult to use). The most important thing to understand is when to use it and then get lots of practice. It is useful to get fluent in applying The Chain Rule, as this will save you lots of time in an exam. This is especially true since some functions are composed of more than two functions and The Chain Rule is often used as part of a bigger question that use other rules ( Product and Quotient Rule ) or questions about Related Rates of Change or  Implicit Differentiation.

Key Concepts

On this page, you should learn about

  • differentiating composite functions using the chain rule
 

Essentials

The following videos will help you understand all the concepts from this page

Why and How

The following video explains why we need The Chain Rule and how to use it. There will be two examples in which we will find the derivative of \((3x+1)^4\) and \(e^{3x^2}\)

Differentiating  [f(x)]n

In the following video, we will look for some simple patterns so that we can quickly differentiate functions in the form [f(x)]n

 

Differentiating ef(x) and ln[f(x)]

In the following video, we will look for some simple patterns so that we can quickly differentiate functions in the form ef(x) and ln[f(x)]

 

Summary

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Test Yourself

We have seen that \(\frac{d}{dx}[f(x)]^{n}=n\cdot f\,'(x)\cdot[f(x)]^{n-1}\)

Here is a quiz that will get you to practise deriving simple expressions using this quick rule


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We have also seen that

  • \(\frac{d}{dx}e^{f(x)}=f\,'(x)e^{f(x)}\)
  • \(\frac{d}{dx}ln[f(x)] = \frac{f\,'(x)}{f(x)}\)

Here is a quiz that will get you to practise deriving simple expressions using these quick rules


START QUIZ!

Here is a mixed quiz that will get you to practise all the skills deriving simple expressions using the Chain Rule


START QUIZ!
MY PROGRESS

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