On Partial Derivatives

(In Mathematics)

Prereqs

This article assumes you know what a derivative is with respect to calculus in Mathematics, as a partial derivative is just a special case of the derivative.

Review

You can take the derivative of a function f to be called (df/dx) ie. “df over dx”.

You can see in the illustration below that (df/dx)(2) ie. “the derivative of f of x [f(x)] at x=2” that (df/dx) notation kind of shows what’s going on. dx is “distance in x” you can see in the yellow ink, at x=2 we are doing just a tiny little nudge in x axis to the right, and df is “distance in f of x” you can see we are doing just a tiny little nudge upward in f(x) axis (often called the “y axis”) upward.

[2] Partial Derivatives Khan Academy. https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction

Definition

a derivative of a function of two or more variables with respect to one variable, the other(s) being treated as constant. [1] Basically a partial derivative is just a type of derivative, it follows all the same rules as a regular derivative.

What does the partial derivative tell us?

What does the partial derivative tell us?
Partial derivatives tell you how a multivariable function changes as you tweak just one of the variables in its input.