Question

What does the \[\nabla\]symbol denote in mathematics? What does the \[\nabla\]symbol denote in mathematics? @Mathematics

Answer 1

del

Answer 2

what does del denote?

Answer 3

commonly denotes del f, which is the gradient vector

Answer 4

so \[\nabla x\]is the derivative of vector x?

Answer 5

is it okay if I say \[y = x\]\[\frac{\nabla y}{\nabla x}=1\]?

Answer 6

in that notation, it would not be clear that x is a vector. but del f is the partial derivatives of each component

Answer 7

so if f(x,y,z) the del f is (df/dx,df/dy,df/dz)

Answer 8

del y/del x does not necessarily equal 1.

Answer 9

why not?

Answer 10

del y is a vector so is del x, so division of the two vectors doesn't make any sense

Answer 11

that is true, convention is that we do not divide vectors, even if they are in the same space

Answer 12

I thought it made as much sense as \[\frac{dy}{dx}\]

Answer 13

but those are scalar quanities

Answer 14

*quantities

Answer 15

if y is a function, that makes sense

Answer 16

if your function is y(x)

Answer 17

dy/dx = yprime

Answer 18

btw dy/dx isn't division, it's just notation that specifies that you're deriving y(x) with respect to x

Answer 19

if that notation confuses you, then use \[\Large D_{x}(y(x))\] to denote that you're deriving y(x) with respect to x

Answer 20

\[y \prime (x)\]