The Differentiation Onion Method for Chain Rule – Part 2

In Part 1, I introduced “Onion Method for differentiation” as a way to quickly apply the Chain Rule.

Onion2 - 01.png

In this article, I discuss another example (see above).

Onion2 - 02.png

First, draw the “onion” in pencil (shown as red above). Now we “peel the onion” from the outer layer. The outer layer is “cos”, and that becomes “-sin” when you differentiate it. Copy and paste the inner expression (the yellow patch) wholesale. Put a dot for multiplication. Now differentiate the inner expression. This is just -4. Now we tidy up. The two negatives cancel each other. We write the factor 4 to the left of the “sin”. Done!

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