Derivatives... How? (NancyPi)

Quotient Rule Proof

Day 162 — 365 Problems for 365 Days AP Calculus derivative with logarithms (quotient rule): d/dx [ x / ln(x) ] This is a high-yield calculus derivative because it mixes a rational expression with a natural log. The cleanest path is the quotient rule, but it also reinforces the key fact that d/dx ln(x) = 1/x. This exact pattern shows up in optimization, related rates, and in simplifying harder derivatives. Project Mentor helps high school students with AP self-study plans, competition prep, and r