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If anyone could explain step by step how following problem is done, it would be greatly appreciated!
If F(x,y,z)=0 defines implicitly z = f(x,y), then ∂z/∂x = -F_x/F_z and ∂z/∂y = -F_y/F_z.
Find ∂z/∂x and ∂z/∂y as functions of x, y, and z, assuming that z=f(x,y) satisfies the given equation:
x^3 + y^3 + z^3 = xyz
Last edited by meebo0129 (2007-07-30 00:38:18)
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just set
F(x,y,z)=x^3 + y^3 + z^3 -xyz
X'(y-Xβ)=0
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If F(x,y,z)=0 defines implicitly z = f(x,y), then ∂z/∂x = -F_x/F_z and ∂z/∂y = -F_y/F_z.
Differentiate F implicitly wrt x keeping y constant, using the chain rule for partial derivatives.
Now differentiate F implicitly wrt y keeping x constant in the same way.
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