Prove: If F x , y , z = f x , y , z i + g x , y , z j + h x , y , z k is a conservative field and f , g , and h are continuous and have continuous first partial derivatives in a region, then ∂ f ∂ y = ∂ g ∂ x , ∂ f ∂ z = ∂ h ∂ x , ∂ g ∂ z = ∂ h ∂ y in the region.
Prove: If F x , y , z = f x , y , z i + g x , y , z j + h x , y , z k is a conservative field and f , g , and h are continuous and have continuous first partial derivatives in a region, then ∂ f ∂ y = ∂ g ∂ x , ∂ f ∂ z = ∂ h ∂ x , ∂ g ∂ z = ∂ h ∂ y in the region.
Prove: If
F
x
,
y
,
z
=
f
x
,
y
,
z
i
+
g
x
,
y
,
z
j
+
h
x
,
y
,
z
k
is a conservative field and f, g, and h are continuous and have continuous first partial derivatives in a region, then
∂
f
∂
y
=
∂
g
∂
x
,
∂
f
∂
z
=
∂
h
∂
x
,
∂
g
∂
z
=
∂
h
∂
y
in the region.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY