University of Oxford Mathematician Dr Tom Crawford explains how partial differentiation works and applies it to several examples. Try the exercises for yourself here.
We begin by looking at the limit definition of a normal or ‘full’ derivative which we use to motivate the idea behind partial derivatives. Once the partial x and partial y derivatives are defined, we then calculate them for a polynomial function f(x,y) which defines a 3D surface. This is plotted in the Maple Calculator App to help to visualise the changing behaviour of the function in different directions. You can download the app for free from Google Play and the App Store.
We then look at a more complicated example involving exponential and trigonometric functions, which requires the use of the product rule and the chain rule. You can find more questions for you to work through in the Maple Learn worksheet created by Tom here.