Partial Derivatives

Imagine you're faced with the following function...

...and asked to take the derivative with respect to y.

How can you do that, considering that we've got multiple variables here (x, y)?

We can accomplish this with partial derivatives!

Partial derivatives are used to take derivatives of functions that have multiple variables.

Recognizing notation

Recall in What is a derivative? we detailed the following notations for derivatives (with one variable, x):

NotationDerivative of function

How does this differ from partial derivatives?

Let's imagine we were taking the derivative of f(x, y) with respect to y. That'd look like so:

NotationDerivative of function
Lagrangef'(x, y)
Eulerfy(x, y)

A couple important things to note about each of these...


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