Download Product and Quotient Rule Practice 1

Product and Quotient Rule Practice 1
1. Let’s try to apply these rules. Find the derivatives for each of the following.
a. f(x) = x2sin(x)
b. y  ln(x)  2x3
c. f(x) = excos(x)
d. f(x)  4x3 (x2  4x)
2. y = xsin(x) – 2xcos(x), determine
dy
.
dx
3. Determine each of the following.
a. Find f’(x) if f(x) = 4x 3  sin( x)
b. Find h’(2) if h(x) = 5x3 – 2x2
4. Determine the derivatives of each of the following.
a. y = 5sin(x)
b. y = 5xcos(x)
c. y = 5sin(x)cos(x)
6. Use the table to answer the given questions. Show your calculus!!!!
x
f
f’
g
g’
a. If h(x) = f(x)g(x), determine h’(5).
2
5
-3
2
-1
2
1
2
3
3
4
-2
b. If p(x) = 3x  g(x) , determine p’(2).
c. Determine the equation of the line tangent
to the graph of g(x) at x = 2.
7. Let’s try to apply this rule. Find the derivatives for each of the following.
a. f(x) 
5x  2
x2  1
b. f(x) 
sin x
x2  4
c. f(x) 
ex
sin x
8. Use the table to answer the given questions. Show your calculus!!!!
x
f
f’
g
g’
g(x)
2x
2
5
-3
2
-1
a. If p(x) 
,
b. If p(x) 
, determine
f(x)
f(x)
3
determine p’(2)
p’(5).
1
2
3
4
-2
2
--------------------------------------------------------------------------------------------------------------9. If f(x) = tanx, determine f’’(x)
10. If f(x) = cotx, determine 3f’(x)
--------------------------------------------------------------------------------------------------------------11. If f(x) = secx, find

dy
at x =
dx
4
12. If f(x) = cscx, find
13. Determine the equation of the tangent line of f(x) = sinx, at x =

.
3
d2y
dx