Remembering how to differentiate – Secrets of the Mathematical Ninja

The Mathematical Ninja makes ample use of mnemonics to remember how to do just about everything. He was quite upset when Pluto was demoted, because "My Very Easy Mnemonic Just Serves Up Nine" doesn't make any sense.

In particular, the Mathematical Ninja has a creed. A strict set of rules to live by. And I'm not just talking about the Bushido. No, sir. He lives by the creed:

Drink some coffee. Make some more coffee.

It also serves as a reminder of how to differentiate trig functions:

  • Drink : Differentiate
  • Some : $\sin$ (differentiates to...)
  • Coffee : $\cos$ (differentiates to...)
  • Make some: $-\sin$ (differentiates to...)
  • More coffee: $-\cos$

Easy! So you differentiate $-\sin(x)$ to get $-\cos(x)$.

The other thing to remember: when you differentiate things, you tend to times. If you differentiate $\cos(2x)$, you get $-2\sin(2x)$.


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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I teach in my home in Abbotsbury Road, Weymouth.

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