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.

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, divergence, curl, and more!

For the given gradient vector we can understand that any vector in its own direction have maximum dot product. But how does it proves the gradient vector is itself the direction of maximum ascent.

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Learn how the gradient can be thought of as pointing in the "direction of steepest ascent". This is a rather important interpretation for the gradient. Created by Grant Sanderson.

The gradient of f, with our little del symbol, is a function of x and y. And it's a vector-valued function whose first coordinate is the partial derivative of f with respect to x.

Course: Multivariable calculus > Unit 2 Lesson 3: Partial derivative and gradient (articles) Introduction to partial derivatives Second partial derivatives The gradient Directional derivatives (introduction) …

Given scalar field, what is the gradient?

Divergence measures the change in density of a fluid flowing according to a given vector field.