Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. div( ϕ F) = ϕ div F + ∇ ϕ ⋅ F
Let k be a constant, F = F( x , y , z ) , G = G( x , y , z ) , and ϕ = ϕ ( x , y , z ) . Prove the following identities, assuming that all derivatives involved exist and are continuous. div( ϕ F) = ϕ div F + ∇ ϕ ⋅ F
Let k be a constant,
F
=
F(
x
,
y
,
z
)
,
G
=
G(
x
,
y
,
z
)
,
and
ϕ
=
ϕ
(
x
,
y
,
z
)
.
Prove the following identities, assuming that all derivatives involved exist and are continuous.
Consider a function f: R? →
R°, the derivative of f isa
O 3 x 3 matrix
O 3 x 2 matrix
O 2 x 3 matrix
O 2 x 2 matrix
O 3 x 5 matrix
O 2 x 5 matrix
O 5 x 3 matrix
O 5 x 2 matrix
Let f(x, y) = V xy. Find the derivative of f.
af
1
ду
2
Let v = (3,4, 12) . Find the directional derivative of f(r, y, z) = x – y? +32³ in the direction of v.
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY