Directional Derivatives

But then there's this thing called the Gradient...

Directional Deriviatives

When finding directional derivatives, make certain that the vector you are given is a unit vector!If it is not a unit vector, you must find its corresponding unit vector first, by determining the length and dividing each component by the length.

Here's the Definition

Note in this example that we had to find the unit vector by using cosine and sine of the given angle.

The gradient of a multivariable function is simply the vector of partial derivatives and is denoted by this symbol.

Now that we know what a gradient is, we can think of the directional derivative as a simple dot product!

Watch this video for more explanation of the gradient!

So, our formula for the directional derivative is: