Went to solve a few derivative problems using the difference quotient before heading to sleep.
Back at the traditional BSEE locally, it was not even called Difference Quotient but naively as “Three-step Procedure”. The mistake in the program was to treat the Difference Quotient as a second hand citizen hence we just tackled it for a brief period of time and left. The focus was not the use of the Difference Quotient but using the derivative formulas which are an abstraction higher than the Difference Quotient.
The interesting part is when it comes to solving the derivative of sin(x). Back in the BSEE we memorize the derivative formulas, so it is quick since it is already an abstraction. The derivative formula for sin(x) is
\[ \frac{d}{dx}\sin(x)=\cos(x) \]That one is quick but the only problem with that, you lose the intuition from first principles. Solving the derivative of sin(x) last night worked my rusty trigonometric identities and rusty solving for system of equations with the help of LLMs. Phi4-mini showed me one way to solve it while ChatGPT showed me another way.
Phi4’s method was more advanced and difficult to follow as it involves not only trigonometric identities with sum and difference of angles including solving for system of equations. ChatGPT was more simple and stayed with strictly trigonometric identities only. Both gave me the intuition on the derivative of sin(x) and similar derivatives for simple transcendental functions in trigonometry.
More practice problems later.
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