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.

- Chain Rule
- Product Rule
- 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 with respect to x:

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

so

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 so now, we don't even have to use product rule :

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

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

Certainly hope it is useful.

:-)

alwaysLovely

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

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:

February 24th, 2011 at 12:54 am

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