What is a partial derivative? @drpeyam

Uploaded March 2025 | Updated September 2026, 1 week ago

What is a partial derivative?

Welcome to one of the most important concepts of multivariable calculus: partial derivatives. It's partially derivative, but a whole lot of fun! Here we introduce the notion of partial derivative, which is the slope of a function of several variables, but in different directions. This concept is fundamental to the study of partial differential equations, which is the content of one of the playlists. Along the way we mention Clairaut's theorem, which tells us that mixed partial derivatives are equal, under certain circumstances.

Introduction to PDE playlist: youtube.com/playlist?list=PLJb1qAQIrmmBeGlVY_V3XKYd9Bwa6GcMs

Partial derivatives playlist: youtube.com/playlist?list=PLJb1qAQIrmmCKSZwoHh-Il6s9-68CfLCu

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$Solving the logistic equation Solving the logistic equation. What does the fox say? Here I solve a differential equation using separation of variables and partial fractions and integrals. It models the population of bunnies but with a limited factor. It gives a surprisingly good model approximation of populations like in Belgium. Enjoy this calculus adventure Subscribe to my channel: https://youtube.com/drpeyam TikTok: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$

$Half integral of x Defining the half integral, which is halfway between a function and its integral. Done by analogy with half derivatives, by finding formulas for the derivatives of power functions. It uses the factorial which is then generalized to the gamma function with Gaussian integrals. I also mention trig functions and applications to broken processes. This is a delight for any calculus student or anyone who is interested in fractional derivatives. 0:00 Introduction 0:30 Analogy 2:58 Gamma Function 5:00 Half integral of x 9:37 Properties and Applications Half Derivative: https://youtu.be/gaAhCTDc6oA YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$