**Question**

**Introduction**

The
differentiation of the secant function is not taught directly as part of the
Additional Mathematics syllabus. It can
be derived from known facts. I first
show the standard application of the (extended) Chain Rule for novices, and
then show a more effective way of applying the chain rule, which I called the
“Onion Method”. This looks like peeling onions
or unpacking Matryoshka dolls (“Russian dolls”).

**Reminders**

**Solution 1**(for beginners)

**Solution 2**(a more expedient way)

**Final Remarks**

When we
peel onions, we peel from the outer layer inwards. Likewise, when we have a composite function,
we differentiate from the outer layer first, and then work to the inner layers. Every time we differentiate a layer, we write
down the changed layer and then copy and paste everything within that layer. With regular practice, this should become second
nature.

For another example of the “onion”, take a look at the derivative of the arcsecant function.

For another example of the “onion”, take a look at the derivative of the arcsecant function.

H04. Look for
pattern(s)

H05. Work
backwards

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

*****GCE ‘A’ Level H1 Mathematics

*****GCE ‘A’ Level H2 Mathematics (revision)

*****International Baccalaureate SL & HL Mathematics

* AP Calculus AB & BC

* other syllabuses that calculus

* anyone who loves to learn!
Actually, instead of memorising this as a procedure to be followed, it would be good if students can figure out the procedure on their own. That is another level of thinking and learning. Can you think of a common mathematical difficulty, and figure out yourself a procedure for solving it in your own words?

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