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Homework Statement
Calculate the gradient of:
(a) V1=6xy2xz+z
(b) V2=10ρcos(phi)ρz
(c) V3=(2/r)cos(phi)
Homework Equations
The Attempt at a Solution
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You did not write "just del". You wrote deldot. The dot was wrong. You can write del f or you can write grad f. Same thing. (But deldotF is OK whereas del F or grad F are not.)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))
Yes, ∂(2xz)/∂y = 0.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.
Was what 6y i + k ?dang I felt it might have actually been right. was it simply this 6yi+k
I said use V1, not f.∇V1=(∂f/∂x)i+(∂f/∂y)j+(∂f/∂z)k= 6y i + k
What about ∂(2xz)/∂x?∂(V1)/∂x = 6y i sorry I forgot the "i" in the previous post.
Better.6y2z i
Right!(6y2z)i + (6x)j + (12x)k
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 1_{ρ} and 1_{Φ} which is still standard.for V2 (10cos(phi))z)i(10sin(phi))j(ρ)k
Problem here.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 1_{r}, 1_{φ} and 1_{θ}.for V3 ((2/r^2)cos(phi))i((2sin(phi))/(r^2sin(theta)))k