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For the first one, the derivative and integral of e^x is just e^x. For the second one, limits and power rule are only the basics of the average calc class. For the third one, as I said, d/dx of e^x = e^x. e^x is the only function that has this property. For the last one, cos(60) and sin(30) both equal 1/2, and also tan(26.565) is also about 1/2. . . . . #calculusmemes #calculus #mathmemes
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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
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Day 171 — 365 Problems for 365 Days AP Calculus limit with exponential and trig: lim x->0 (e^x - 1) / sin(x) This is a classic 0/0 limit that’s perfect for L’Hôpital’s Rule and also connects to two key calculus facts: the derivative of e^x is e^x, and the derivative of sin x is cos x. It’s a great warm-up problem for limits, derivatives, and exam-style simplification. Project Mentor helps high school students with AP self-study plans, competition prep, and research/internship guidance — see my b
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