How do you define a Partial Derivative?

Daily Dose 024 | Mathematics

How do you find a Partial Derivative?

Define a Partial Derivative, what’s the point?

Welp, quite a bit.

We live in a three dimensional space where our designs need to operate safely and efficiently in the midst of a wide range of variables.

Of course we can’t design to maximize efficiency for every variable, but we can for the most critical.

Partial derivatives, loosely speaking, allow us to define how much a system (multi-variable function) will change when holding other variables constant.

If we stiffen the columns on a high rise at some point and increase the wind load, will the sway be limited to acceptable magnitude?

If we expanded the lifespan of this product by a year, will the economic return be worth the input?

So whether or not you see the value in working with Partial Derivatives in the real world, it’s something we need to know for the FE Exam.

We at Prepineer are going to make sure you are ready for them.

In this video, we dive in to a FE Exam Practice Problem in the subject of MATHEMATICS, specifically dealing with how to define a Partial Derivative.

Key Definition

What is PARTIAL DERIVATIVES?

In MATHEMATICS, the PARTIAL DERIVATIVE of a function of several variables is its derivative with respect to one of those variables, with the others held constant.

This is opposed to the TOTAL DERIVATIVE, in which all variables are allowed to vary.

The reason for a new type of derivative is that when the input of a function is made up of multiple variables, we want to see how the function changes as we let just one of those variables change while holding all the others constant.

So how can you go about defining a partial derivative?

Check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, with Love, Prepineer

Video Review

How to define a Partial Derivative