so what you are saying is that instead of just del I should have used del f for notation?
(∂f/∂x)x+(∂f/∂y)y+(∂f/∂z)z (where x, y, and z should be x(hat), y(hat), and z(hat))
so if I am right which I probably am not then (a) 6yUx+(-0)+zUz the reason I put 0 is the the partial derivative of -2xz with respect to y is 0 correct since there is no y term.
so what you are saying is that instead of just del I should have used del f for notation?
(∂f/∂x)x+(∂f/∂y)y+(∂f/∂z)z (where x, y, and z should be x(hat), y(hat), and z(hat))
You did not write "just del". You wrote del-dot. The dot was wrong. You can write del f or you can write grad f. Same thing. (But del-dot-F is OK whereas del F or grad F are not.)
Your expression for grad f is correct for Cartesian coordinates x,y,z. I use i, j , and k for the unit vectors. I also use bold type for all vectors.
When you get to V2 and V3 the expressions for grad V are very different from Cartesian. V2 is using cylindrical and V3 is using spherical.
so if I am right which I probably am not then (a) 6yUx+(-0)+zUz the reason I put 0 is the the partial derivative of -2xz with respect to y is 0 correct since there is no y term.
Yes, ∂(-2xz)/∂y = 0.
No, you are not following your formula in post 3 for V1.
Don't keep changing your notation for the unit vectors. Use i j k why not.
Tell you what, start over with your expression for grad V1 from your post 3, use i j k unit vectors, and let's see if we can't figure this one out. Remember to use V1, not f.
Right, except you can't use i and j for the ρ and phi unit vectors. Since I don't know how to put hats over letters I would use 1ρ and 1Φ which is still standard.
for V3 ((-2/r^2)cos(phi))i-((2sin(phi))/(r^2sin(theta)))k
Problem here.
With V2 I noticed the angle phi was used; I believe for cylindrical coordinates that angle is usually denoted by theta.
So I have to assume phi is the same angle for V3 as it was for V2, i.e. the angle between the x-y plane and the z axis, in which case grad V3 looks wrong. Do you know which angle is the one made with the z axis and which is in the x-y plane? Then I could check grad V3 also.
Anyway, you seem to be with the program here and have done quite well.
for V3 ((-2/r^2)cos(phi))i-((2sin(phi))/(r^2sin(theta)))k
Correct, except again you don't use i j k as unit vectors for spherical coordinates. Use 1r, 1φ and 1θ.
V2 shoud have used θ instead of φ. It's not good for φ to be the z-axis angle in one coordinate system and the x-y angle in another. I would explain that to your instructor.
