(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
.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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