Calculus Section 4.6
Page31
4.6b
More on Related Rates
Sometimes more than two quantities are changing within a certain relationship.
At this
point, you must consider the product rule, the quotient rule, and the chain rule when
differentiating to express how different rates of change are related.
Areas
Rectangle:
A
=
lw
Find an equation that relates
dA
dt
,
dl
dt
, and
dw
dt
Triangle:
A
=
1
2
bh
Find an equation that relates
dA
dt
,
db
dt
, and
dh
dt
Volumes
Cylinder:
V
= π
r
2
h
Find an equation that relates
dV
dt
,
dr
dt
, and
dh
dt
Cone:
V
=
1
3
π
r
2
h
Find an equation that relates
dV
dt
,
dr
dt
, and
dh
dt
Cone:
V
=
1
3
π
r
2
h
Find an equation that relates
dV
dt
and
dr
dt
if
h
is a
constant.
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Page 32
Sphere:
V
=
4
3
π
r
3
Find an equation that relates
dV
dt
and
dr
dt
Rectangular box:
V
=
lwh
Find an equation that relates
dV
dt
,
dl
dt
,
dw
dt
, and
dh
dt
Lengths of Sides
Right Triangle:
x
2
+
y
2
=
z
2
Find an equation that relates
dx
dt
,
dy
dt
, and
dz
dt
Right Triangle:
x
2
+
y
2
=
z
2
Find an equation that relates
dx
dt
and
dz
dt
if
y
is a
constant.
Diagonal of a rectangle:
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 Spring '10
 John
 Calculus, Chain Rule, Derivative, Product Rule, Quotient Rule, The Chain Rule, Trigraph, dt dt, DT DT DT, dr dh

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