The gradient stores all the partial derivative information of a multivariable function. But it's more than a mere storage device, it has several wonderful interpretations and many, many uses.

The gradient is a way of packing together all the partial derivative information of a function. So let's just start by computing the partial derivatives of this guy.

Take a moment to delight in the fact that one single operation, the gradient, packs enough information to compute the rate of change of a function in every possible direction!

When you expand it, the gradient would have five components, and the vector itself would have five components. So, this is the directional derivative and how you calculate it.

A more thorough look at the formula for directional derivatives, along with an explanation for why the gradient gives the slope of steepest ascent.

Instead of finding minima by manipulating symbols, gradient descent approximates the solution with numbers. Furthermore, all it needs in order to run is a function's numerical output, no …

Here we go over many different ways to extend the idea of a derivative to higher dimensions, including partial derivatives , directional derivatives, the gradient, vector derivatives, …

Notation and formula for divergence The notation for divergence uses the same symbol " ∇ " which you may be familiar with from the gradient. As with the gradient, we think of this symbol …

The way we compute the gradient seems unrelated to its interpretation as the direction of steepest ascent. Here you can see how the two relate.

Gradient is another word for slope. That means that finding the gradient (slope) involves a function and outputs a vector using nabla, which can be considered a function