Friday, November 27, 2015
[AM_20151127DF2D] Differentiation with Chunking and Elimination
Although this looks like a differential equation question, the student is not required to solve the differential equation. The requirement is just to derive the equation. This would be a challenging question for secondary 4 (~ grade 10) students taking Additional Mathematics or their counterparts in Integrated Programme schools.
One way to do this is to differentiate the given equation once and again and just verify the equation by substitution. The problem is that when we repeatedly apply the Product rule
the terms tend to sprawl. A way to keep things neat is to try to recognise chunks and also use elimination.
After differentiating once, we notice that 10xe2x is twice of 5xe2x, and this allows the simplification in . The second differentiation yields 10e2x which, we notice, is twice of 5e2x. We can get rid of that term. Multiplying equation  by 2 gives 10e2x in equation , which matches nicely with the same term in . So we can eliminate that term via elimination. After that, we just need to rearrange things to get the final equation.
H04. Look for pattern(s)
H05. Work backwards
H10. Simplify the problem
H11. Solve part of the problem
H13* Use Equation / write a Mathematical Sentence
* GCE ‘O’ Level Additional Mathematics, “Integrated Programme Mathematics”
* GCE ‘A’ Levels H2 Mathematics (revision)
* AP Calculus AB / BC (revision)
* University / College calculus (revision)
* other syllabuses that involve differentiation
* any learner interested in calculus