Consider The Following. W = Yz/X, X = Θ2, Y = R + 7θ, Z = R − 7θ (A) Find ∂W/∂R And ∂W/∂Θ By Using The Appropriate Chain

Consider The Following. W = Yz/X, X = Θ2, Y = R + 7θ, Z = R − 7θ (A) Find ∂W/∂R And ∂W/∂Θ By Using The Appropriate Chain

1) Consider the following.

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w = yz/x, x = θ2y = r + 7θz = r − 7θ

(a) Find ∂w/∂r and ∂w/∂θ by using the appropriate Chain Rule.

w
r
=
w
θ
=

 

(b) Find ∂w/∂r and ∂w/∂θ by converting w to a function of r and θ before differentiating.

w
r
=
w
θ
=

 

2) Evaluate fxfy and fz at the given point.

f(xyz) = x2y3 + 7xyz − 5yz, (−1, 2, 1)

fx(−1, 2, 1) =
fy(−1, 2, 1) =

 

3) For f(xy), find all values of x and y such that fx(xy) = 0 and fy(xy) = 0 simultaneously.

f(xy) = x2 + 4xy + y2 − 18x − 12y + 14

(xy) =

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