The symbol itself is called del, but what its meaning is related to the gradient. This symbol can be used in different ways for different meanings.

For example if you have del dot vector, it means you are taking the dot product of <d/dx, d/dy, d/dz> with the vector. This is known as the “divergence.” So div(<x,x^2,y+z)> = dx/dx + dx^2/dy + d(y+z)/dz = 1 + 0 + 1 = 2

If you have del cross vector, it means you are taking the cross product of <d/dx, d/dy, d/dz> with the vector. This is known as the “curl.”

However if you have del next to a function f, then you are taking the actual gradient of the function f. That is, you are creating the vector <df/dx, df/dy, df/dz>.

There are others like del squared dot vector or del squared cross a vector, but I don’t really remember much about those.

It means gradient and indicate the direction in which function is increasing most rapidly at a certain point, and magnitude of gradient vector indicated the magnitude of change in that direction.

You can also use gradient vector to calculate magnitude of change in direction of unit vector u by taking dot product of gradient vector and u.

If gradient at a certain point = zero-vector, then function is not increasing at all at that point, and therefore point is local minimum, local maximum, or saddle point.

Do it yourself.

Or give your teacher a bj.

Sound familiar? Back off freak