I introduced Quotient Rule to the class last week so today we continued with it. Quotient Rule is actually very easy to use and should not be replaced by the Product Rule, even though it’s very convenient for students to write a fraction as a product of two terms.
What students find difficult is in simplifying the resulting expression, which often consists of fractions within fractions, with some terms having a square root sign over it. Of course there is a ‘trick’ to get the factorisation done quickly and correctly, but it’s too cumbersome for me to demonstrate here. More importantly, this difficulty that students often face highlights the point that I’ve posted earlier, that Sec 1 and Sec 2 Algebra is VERY IMPORTANT.
For the next lesson, I’ll be going into the Second Derivative as well as Application of Differentiation to curves, tangents and normal. We may be covering the Chain Rule if we have time.
Rgds,
Ilyasa, M.Ed, PGDE, ex-MOE Math and Physics teacher (hp: 97860411)
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Sec 4 A. Math Reflections sat1415 19/01/2013 – Differentiation
This was our third lesson in Jan. We did the Product Rule for Differentiation after spending the last two sessions doing the Basic Rule and the Power Rule (a subset of the chain rule).
I told students to differentiate directly, in line, and not use the “let u = f(x) and v = g(x)” which is longer, more confusing and can cause more careless mistakes.
Now they are able to perform dy/dx = f(x)g'(x) + g(x)f'(x) quite quickly without introducing new variables such u and v which can be quite clumsy. Most of the time, finding dy/dx is part of a larger question, so it is unwise to make this part too long.
I ended the lesson with an intro to the Quotient Rule. Again, I don’t recommend the use of u’s and v’s and instead differentiate directly in line. We’ll be practising the Quotient Rule in the next session.
Again I tell students that Calculus is almost one-third of the A. Math syllabus, so if you want to get A1 you have to master Differentiation and Integration, which, in my opinion (and students hate it every time I say it), are amongst the easiest of topics in A.Math.
However, Integration at the A-Levels (H2 Math) can be quite difficult. But we’ll cross the bridge when we come to it. : )
Ilyasa, M.Ed, PGDE, ex-MOE teacher
(hp: 97860411)
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For our latest timetable, click here =>
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