f the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the points whe az Fy az Fv

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the points where F₂ #0, the following equations are true.
əz
Fx
əz
Fy
and
?x
F₂
ду
Z
Use these equations to find the values of az/ax and az / ay at the given point.
z³ - 2xy + 3yz+y³ - 69 = 0, (1,4,1)
dz
(Type an integer or a simplified fraction.)
dx
=
|(1,4,1)
Transcribed Image Text:If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the points where F₂ #0, the following equations are true. əz Fx əz Fy and ?x F₂ ду Z Use these equations to find the values of az/ax and az / ay at the given point. z³ - 2xy + 3yz+y³ - 69 = 0, (1,4,1) dz (Type an integer or a simplified fraction.) dx = |(1,4,1)
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