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WhyNot Science | Why the Derivative of eˣ Stays eˣ A tiny change in x, a tiny change in the output—and the rate of change always matches the value of e^x... | Instagram
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Phyxon on Instagram: "A function that differentiates itself — sounds impossible, right? 🤔 Meet the only number in the world that stays the same… even after differentiation 👑 Let’s prove why 𝑑/𝑑𝑥 (eˣ) = eˣ using the First Principle of Derivatives 📘 We start with: 𝑑/𝑑𝑥 f(x) = lim (h → 0) [(f(x + h) − f(x)) / h] Now substitute f(x) = eˣ ⤵️ 𝑑/𝑑𝑥 eˣ = lim (h → 0) [(e^(x + h) − eˣ) / h] Factor out eˣ ⤵️ = eˣ × lim (h → 0) [(eʰ − 1) / h] And this magical limit equals 1 lim (h → 0) [(eʰ − 1)
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