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 here. (Examples included) I would like to share one question from my A-Math Ultimate Leap Programme (weekly coaching class) which has 2 different approaches to solve it.

Example:

differentiation-qn

Very often, I notice students will jump into Quotient rule whenever a fraction is given. Just like this student here:

differentiation-qn-quotient-rule

May I suggest that you pause for 3 seconds to think about the approach. Ask yourself 'Is there anything I can simplify?'

Here's another student who pauses:

differentiation-qn-simplified

Notice this student spends his time simplifying before applying chain rule in differentiation.

I hope you enjoy this example. Both students are correct in their answers, which one do you prefer more? A or B?

Related Posts:

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! :)

2 Responses to A-Math: Differentiation Shortcut Lies In Pausing & Simplifying
  1. :)
    February 6, 2010 | 12:47 am

    I wasn't even aware of the shortcut.
    My teacher just taught v differentiate(u) - (u) differentiate(v)divided by v^2
    It was a a long process as i still have to take time to factor out. I realised Student B's method is much shorter, and will ensure better accuracy of the answers. The example really helped a lot ! :)

    Reply

  2. Nguy?n ??c Tùng
    February 7, 2010 | 8:17 pm

    There is another way to solve this problem.
    I have been leart it in my school.
    But when I solved this problem in that way. It was very long and hard.

    The example of student A, I think is the best.

    I like it.

    Reply

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