(a) Let w be a differentiable function of x 1 , x 2 , x 3 , and x 4 , and let each x i be a differentiable function of t . Find a chain-rule formula for d w / d t . (b) Let w be a differentiable function of x 1 , x 2 , x 3 , and x 4 , and let each x i be a differentiable function of υ 1 , υ 2 , and υ 3 . Find chain-rule formulas for ∂ w / ∂ υ 1 , ∂ w / ∂ υ 2 , and ∂ w / ∂ υ 3 .
(a) Let w be a differentiable function of x 1 , x 2 , x 3 , and x 4 , and let each x i be a differentiable function of t . Find a chain-rule formula for d w / d t . (b) Let w be a differentiable function of x 1 , x 2 , x 3 , and x 4 , and let each x i be a differentiable function of υ 1 , υ 2 , and υ 3 . Find chain-rule formulas for ∂ w / ∂ υ 1 , ∂ w / ∂ υ 2 , and ∂ w / ∂ υ 3 .
(a) Let w be a differentiable function of
x
1
,
x
2
,
x
3
,
and
x
4
,
and let each
x
i
be a differentiable function of t. Find a chain-rule formula for
d
w
/
d
t
.
(b) Let w be a differentiable function of
x
1
,
x
2
,
x
3
,
and
x
4
,
and let each
x
i
be a differentiable function of
υ
1
,
υ
2
,
and
υ
3
.
Find chain-rule formulas for
∂
w
/
∂
υ
1
,
∂
w
/
∂
υ
2
,
and
∂
w
/
∂
υ
3
.
3. Let f(x) = x² + 3 and g(x)
and [3, 0), respectively.
= Vx – 3 be functions defined on [0, 0)
i. Draw the graphs of f and g on the same plane with the equation y = x. (Use
different colors for each graph, if possible, and label the graphs properly.)
ii. Give an argument about the relationship of the functions f and g. (Write it
in paragraph form with at least 2 sentences.)
Describe and sketch the domain of each function in the image. Describe as a set, showing how conditions between x and y
Suppose that z is a differentiable function of s, t, u, and v. Also suppose
that s, t, u, and v are differentiable functions of x and y. Write the chain rule formula
for дz/дх.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.