1. Find the slope and the equation of the
tangent line to the graph
.
at the point (4,5).
In 2 – 6, find the derivative of
each function.
2. 
.
3. 
.
4. 
(Express
as single fraction, factored completely!)
5. 
.
6. 
7. Use the limit definition to find the
derivative of
.
8. Use the formula 
and
the quotient rule to derive the formula for the derivative of
y
= tan x .
9. Find the second derivatives of
.
10. Find the second and third derivatives of
.
Find 
.
Check your answers with graphing calculator.
11. Find 
by
implicit differentiation: 
.
12.
Find
in
terms of x and y by implicit differentiation:
.
13.
Find the point(s) at which the graph of the equation
.
14. Find all values of x on the graph of
at
which the slope
of the tangent line is 4.
15. As a balloon in the shape of a sphere is
being blown up, the volume is increasing at the rate of 4 cubic inches
per second. At what rate is the radius increasing when the radius
is 1 inch? Given:
16.
A man 6 feet tall is walks at a rate of 5 ft/sec away from a light that
is 15 feet above the ground. When he is 10 feet from the base of
the light,
a) at what rate is the tip of his shadow moving?
b) at what rate is the shadow lengthening?
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