In 1 - 6, find the derivative f'(x).
Be sure answers are simplified.
1.
[Hint: Is the product rule necessary here?]
2.
3.
4.
5.
[Factor completely!]
6.
7. Use the limit definition of
derivative 
to show that
if f(x)
= cos
x,
then
.
8. Use the quotient rule and a
trig identity to show that if
y
= cot
x,
then
In 9 - 10, find
by implicit differentiation.
9.
10.
y
= sin (xy)
11.
Use the calculator to evaluate the derivative of the function
a)
at
x
= 1
b) at
x
= 4.
Explain your work.
12. Find the equation of the
tangent line to the function 
at the point (2,6).
Explain your work.
13. If
,
find
[Do a few derivatives and generalize.]
14.
Sand is falling off a conveyor belt onto a conical pile at the rate of
20 cubic feet per minute. If the diameter of the pile is equal to the
height of the pile at any time, at what rate is the height of the pile
changing when the pile is 15 feet high?
15.
A man 6 feet tall walks at a rate of 10 ft per sec away from a light
that is 20 feet above the ground. How fast is his shadow lengthening
when he is 15 feet from the base of the light?
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