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The Sine Chain Rule (SinCR) &
Cosine Chain Rule (CosCR)
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Below is a diagram example illustrating the use
of MCR, ExpCR, SinCR, CosCR, SinR, MR, and ExpR:
D-Rule Diagram
D-Operator Diagram
Motivation for the Exponential
Chain Rule (ExpCR)
Motivation for the Sine & Cosine Chain Rules ( SinCR & CosCR)
Here are two exercises, similar to the above explanation for the ExpCR, that should be helpful.

DR Exercise 4.