WhyNot Science on Instagram: "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 itself. Eminem spots the pattern, Trump explains the magic. The most iconic function in calculus, broken down in seconds. ⚠️DISCLAIMER⚠️: This is not real audio/video of Eminem or Trump, and They did not actually say or sing the things you see in the video. This is an AI-generated deepfake created purely for entertainment and educa

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)

Mathematisa | Math Animations on Instagram: "✨The Taylor series (or Taylor expansion) of a function is an infinite sum that represents a function like e^x or cos(x) in terms of its derivatives at a single point. When the expansion is at 0, it’s called a Maclaurin series. The sum of the first n+1 terms forms the nth Taylor polynomial, which is a polynomial approximation of the function. As n increases, the approximation becomes more accurate. Taylor's theorem provides estimates of the error in th