Simple Partial Derivatives

Here's a quick lesson on a calculus topic you'll likely see on the Fundamentals of Engineering exam: partial derivatives. You might also see this in Calculus III if you are still completing that coursework. Anyway, if you are pretty good at taking regular everyday derivatives and/or know where to locate the table of derivatives in your Supplied-Reference Handbook, partial derivatives are very easy. Check it out:

Partial derivatives are indicated by the "curly D" notation (as I call it). Where standard derivatives are written with regular-font d's, such as "dy/dx", partial derivatives use curvy scripted d's.


Partial derivatives are used in functions of more than one variable. If you have a function of more than one variable -- for example, y = 3x + 2z -- you need a way to specify that you are only taking the derivative with respect to one variable, and specify which variable. That's where partial derivatives is useful.

The process is simple. Once you determine what you are taking the derivative with respect to, treat the other variable as a constant. Just pretend it's a number and derive as usual. That's it!

So, in the example above (y = 3x + 2z), if you wanted to take the partial derivative with respect to x, the answer is just 3. We pretend z is a constant, and there is no x in that term, so it just falls out. Easy!

Of course there are more complicated examples, but for the purposes of the FE these will generally follow the rules given in your Supplied-Reference Handbook.

Practice Problems:

Click here to see the solutions to these problems.

More practice: Make up your own crazy partial derivative questions, then go to Wolfram Alpha. Type in "partial derivative (2x + .....) wrt x" for example, to solve the partial derivative of the stuff in the parentheses with respect to x.