Derivatives in Multiple Dimensions

Learn to generalize the derivative to solve problems with more than one variable.

So far, we’ve seen how we can draw a function with a single variable. The graph of the function is a curve that follows a particular pattern depending on the formula that describes the function.

This possibility of drawing the function has been very useful. It helped us solve some simple problems and understand the concept of derivatives. We strongly recommend looking at the graph of a function whenever it’s possible. It’s always a good start.

But unfortunately, it’s not always possible to draw the graph of a function. For example, if the function has two variables instead of one, then the graph will be in 3D. The graph of the function is not a line anymore, it’s a region with height, width, and depth.

We can still draw 3D graphs. But what happens when functions have more than two variables? How can we draw a 4D or 5D graph? It’s impossible!

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