Determine whether the statement is true or false. Explain your answer. If z is a differentiable function of x 1 , x 2 , and x 3 and if x i is a differentiable function of t for i = 1 , 2 , 3 , then z is a differentiable function of t and d z d t = ∑ i = 1 3 ∂ z ∂ x i d x i d t
Determine whether the statement is true or false. Explain your answer. If z is a differentiable function of x 1 , x 2 , and x 3 and if x i is a differentiable function of t for i = 1 , 2 , 3 , then z is a differentiable function of t and d z d t = ∑ i = 1 3 ∂ z ∂ x i d x i d t
Determine whether the statement is true or false. Explain your answer.
If z is a differentiable function of
x
1
,
x
2
,
and
x
3
and if
x
i
is a differentiable function of t for
i
=
1
,
2
,
3
,
then
z
is a differentiable function of t and
d
z
d
t
=
∑
i
=
1
3
∂
z
∂
x
i
d
x
i
d
t
Determine whether z is a function of x and y. xz2 + 2xy − y2 = 4
For the functions w = xy + yz + xz, x = 2u +3v, y = 2u - 3v, and z = uv, express
expressing w directly in terms of u and v before differentiating. Then evaluate
ow
du
dw
TE
H
ow
Express and as functions of u and v.
du
mas Calculus Early Transcendentals, 14e
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dv
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using the chain rule and by
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at the point (u,v) =
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Determine the definition set of the function and show the definition set on the coordinate axis.
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