1. Suppose f (x, y, z) is a function of the variables x, y, and z. Each of x = x(t), y = y(t), and df that z = z(t) is a function of t. Create a tree diagram and write down an expression for dt comes from applying the Chain Rule.

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1. Suppose f (x, y, z) is a function of the variables x, y, and z. Each of x = x(t), y = y(t), and
df
z(t) is a function of t. Create a tree diagram and write down an expression for
that
dt
comes from applying the Chain Rule.
2. For the function above, assume that x(0) = 2, y(0) = 1, z(0) = 3, and f (2,1,3) = 5. Also
%3D
assume that x (0) = -7, y' (0) = 13, z' (0) = 11, and fr (2,1,3) = 0, fy (2,1,3) = -9,
fz(2,1,3) = 19. Find the value of
-(2,1,3).
dt
Transcribed Image Text:1. Suppose f (x, y, z) is a function of the variables x, y, and z. Each of x = x(t), y = y(t), and df z(t) is a function of t. Create a tree diagram and write down an expression for that dt comes from applying the Chain Rule. 2. For the function above, assume that x(0) = 2, y(0) = 1, z(0) = 3, and f (2,1,3) = 5. Also %3D assume that x (0) = -7, y' (0) = 13, z' (0) = 11, and fr (2,1,3) = 0, fy (2,1,3) = -9, fz(2,1,3) = 19. Find the value of -(2,1,3). dt
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