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.

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

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!