# Differentiation Basic Techniques

The big thing for Sec 4 A-Math ( Oh yar, since this blog has quite a number of visitors from other countries, I think it is important for me to mention that Secondary 3 - 4 is known as Grade 9 - 10 in other countries) is CALCULUS.

Well, you will hardly find this word in your A-Math textbook but you see a bulk of the chapters dedicated to Differentiation & Integration. These 2 topics are like freezing and melting processes.

Why? Because they are simply opposite of each other !

I am going to talk about the techniques of differentiation.

There are 3 main types for Sec 4 level ; you ought to learn these techniques real well and know when to apply each one of them as application problems follow after the basics.

1. Chain Rule
2. Product Rule
3. Quotient Rule reserved for fractions. * But some fractions can skip this rule

My personal favourite is No. 2 - Product Rule. Well, let's see the technique in action.

Differentiate $y=3 (x^2 + 5)^4$ with respect to x:

Now to do this, you can apply Product Rule - Differentiate Copy + Differentiate Copy

so $\frac {dy}{dx}=0 (x^2 + 5)^4+ 4(x^2 + 5)^3(2x)(3)

=24x(x^2 + 5)^3$

Now from this example, we notice some patterns, if you have a constant ( a fixed number) in front, you can simply focused on differentiating the portion with x involved. For example in this case, Focus on Differentiating $(x^2 + 5)^4$ so now, we don't even have to use product rule :

1. Leave the constant in front
2. Differentiate the portion with x involved by Power Front - Power Down by 1-Differentiate within also known as your Chain Rule. BINGO!

$\frac {dy}{dx}=(3) 4(x^2 + 5)^3(2x)=24x(x^2 + 5)^3$

By realizing this pattern, it will save you some time and less pen ink as well.

Certainly hope it is useful.

:-)

alwaysLovely

Photo by just another paul

### Related Post

2009 Ultimate Leap Programme : Weekly Ongoing Coaching Classes for 'O' level A-Math See Results EVERY Lesson! Thank for being my reader and for always reading my blog post. It means a lot to me and I hope I have been useful in o...
Protected: Differentiation & Integration Solutions (For workshop participants only) Dear participants, Here are the solutions for questions which you are to work on your own. Click on the link to view them. If anyone can't view ...
Effective Learning Tips from SimpleChemConcepts Recently I was following SimpleChemConcepts Effective Learning Tips Series by Sean. They are extremely useful if and only if you apply them on you...
Differentiation of e How to differentiate e^tanx? first of all to differentiate e^anything = (Diff anything)*e^anything so to differentiate e^tanx = (Diff tanx)*e^ta...
A-Math: Differentiation Shortcut Lies In Pausing & Simplifying Differentiation is a big thing in fact major chapter for all Secondary 4 'O' level students. Read all about the basics Differentiation techniques h...

### Ai Ling Ong

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

### 5 Responses to Differentiation Basic Techniques

1. [...] involving exponential (I have written a post on Differentiation of e; post on Basic Differentiation Techniques are available here too [...]

2. [...] Differentiation Basic Techniques [...]

3. [...] all about the basics Differentiation techniques here. (Examples included) I would like to share one question from A-Math Ultimate Leap Programme (weekly [...]

4. ALVIN HO ZHEE XIANG says:

HOW ARE TO THE FOLLOWING :

A) Y = ( X^3 - 4X )^2 ( 3 X^2 - 4 )^ 3

B) Y = ( 7x + 5 )^3 / ( 7x + 1 )

C) f(x) = 10 ( 1 - 2/x )^-2

D) f(x) = 5/(3-7x)^3

thanks.

Reply

Ai Ling Reply:

Alvin,
I just saw your comment!

A) product rule and chain rule
B) quotient rule and chain rule
C) chain rule
D) convert qn to f(x) = 5*(3-7x)^-3; chain rule

Reply