Important topics to know:
• Know how to find the derivative using
The definition of the derivative
The basic rules: constant rule, power rule, etc.
The rules for trigonometric functions
C)
The product rule
o The quotient rule
o The chain rule
o Using implicit differentiation
• Use the derivative to:
o Write the equation of a tangent line through a given point.
o Find the slope of a function at a given point
o Find the point on the function when the slope has a given value.
• Solve Related Rate problems.
Sample Problems:
dv
dx
t\
Find—
I
7
x
+3
y=(4x+2)
(
3
3x—1)
y=3xsinx+cosx
4—1
—
2
y=cot3x
2
xy
I
C/
3 —2 =0
y —3x
2
+x
-
O.2’.
/‘
1(x)
Find the equation to the tangent line to the graph
.
L
2x
—
3x
4 at the point where x
—I.
p
I
‘p
the values of x for afl ointson the graph of f(x)
=
4x
6x
+
7x—i at which the slope of the tangent hoe s
Find the value of y and / in xv + xv
=
4 when x
=
3
2
at a constant rate of 005 inches per
A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing
the radius r is 1.8 inches?
when
changing
h
length
the
is
what
rate
At
second and the volume is always 128ir cubic inches.
I \ -rr h
j
-
The diameter of the base of the cone is
Sand is falling off a conveyor belt onto a conical pile at the rate of 12 cubic feet per minute.
three times the height. At what rate is the height of the pile changing when it is 1 5 feet high?
r1
L
i
=—.r,
h,
3
Gas is escaping from a spherical balloon at the rate of 2 cubic feet per minute, How fast
of the balloon is 0 fcet”
r
I
=
—
3
1
and
£4
4r
,‘
i
the surface area shrinking when the radius