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Day 157 — 365 Problems for 365 Days AP Calculus derivative practice (log derivatives trig simplification): d/dx [ ln(sin x) ln(cos x) ] This looks like two separate chain-rule problems, but the real “aha” is what happens after you differentiate: the trig terms combine into a single compact expression using double-angle identities. Great practice for derivatives, trig identities, and simplifying results (which is where most people lose points). Project Mentor helps high school students with AP se
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Day 161 — 365 Problems for 365 Days AP Calculus limit with trig identities: lim x->0 (1 - cos x) / x^2 This is one of the most important “foundation” limits in calculus (it shows up in derivatives of sin/cos, Taylor series, and tons of contest problems). The fastest approach is to rewrite 1 - cos x using a half-angle identity, then use the classic limit sin u / u -> 1. Project Mentor helps high school students with AP self-study plans, competition prep, and research/internship guidance — see my
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