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Expert-verified Found in: Page 1153 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Notation: Describe the meanings of each of the following mathematical expressions.$\nabla$

The description about mathematical expression $\nabla$ is as following :-

This symbol is called nabla. This is used to represent gradient where gradient is a collection of all partial derivatives.

If a function $F$ has $n$ variables, then its gradient is :-

$\nabla F=\left[\begin{array}{c}\frac{\partial F}{\partial {x}_{1}}\\ \frac{\partial F}{\partial {x}_{2}}\\ \frac{\partial F}{\partial {x}_{3}}\\ ·\\ ·\\ ·\\ \frac{\partial F}{\partial {x}_{n}}\end{array}\right]$

See the step by step solution

## Step 1. Given Information

We have given the following mathematical expression :-

$\nabla$.

We have to describe the meaning of this expression.

## Step 2. Description

We have given the following symbol :-

$\nabla$

In mathematics this symbol is known as nabla. This is upside down triangle delta symbol.

This symbol is used is vector derivative.

The symbol of nabla is used for gradient. That is the gradient of a vector is denoted by nabla role="math" localid="1651155107117" $\left(\nabla \right)$.

Gradient is the collection of all partial derivatives of a multivariate function.

if a function $F$ has $n$ variables, then the gradient is defined and denoted as following :-

$\nabla F=\left[\begin{array}{c}\frac{\partial F}{\partial {x}_{1}}\\ \frac{\partial F}{\partial {x}_{2}}\\ \frac{\partial F}{\partial {x}_{3}}\\ ·\\ ·\\ ·\\ \frac{\partial F}{\partial {x}_{n}}\end{array}\right]$ ### Want to see more solutions like these? 