Given that the functions u = u x , y , z , v = v x , y , z , w = w x , y , z , and f u , v , w are all differentiable , show that ∇ f u , v , w = ∂ f ∂ v ∇ u + ∂ f ∂ v ∇ v + ∂ f ∂ w ∇ w
Given that the functions u = u x , y , z , v = v x , y , z , w = w x , y , z , and f u , v , w are all differentiable , show that ∇ f u , v , w = ∂ f ∂ v ∇ u + ∂ f ∂ v ∇ v + ∂ f ∂ w ∇ w
Given that the functions
u
=
u
x
,
y
,
z
,
v
=
v
x
,
y
,
z
,
w
=
w
x
,
y
,
z
,
and
f
u
,
v
,
w
are all differentiable, show that
∇
f
u
,
v
,
w
=
∂
f
∂
v
∇
u
+
∂
f
∂
v
∇
v
+
∂
f
∂
w
∇
w
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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