M155 Exam 2 Review Sheet
2.5 – Derivatives of Sums, Powers, and Polynomials
• Terminology
Power Function
Polynomial
• Use binomial theorem to compute powers of sums
• Constant Rule
•
d
dx
c
⋅
f
(
x
)
(
29
=
c
d
dx
f
(
x
)
(
29
• Sum Rule
•
d
dx
f
(
x
)
+
g
(
x
)
(
29
=
df
dx
+
dg
dx
• Power Rule
•
d
dx
x
n
( 29
=
nx
n

1
2.6 – Derivatives of Products and Quotients
• Terminology
Rational Functions
• Product Rule
•
d
dx
f
(
x
)
⋅
g
(
x
)
(
29
=
f
(
x
)
dg
dx
+
g
(
x
)
df
dx
OR
•
f
(
x
)
⋅
g
(
x
)
(
29
′
=
f
(
x
)
′
g
(
x
)
+
g
(
x
)
′
f
(
x
)
• Quotient Rule
•
d
dx
f
(
x
)
g
(
x
)
=
g
(
x
)
df
dx

f
(
x
)
dg
dx
g
(
x
)
[
]
2
OR
•
f
(
x
)
g
(
x
)
′
=
g
(
x
)
′
f
(
x
)

f
(
x
)
′
g
(
x
)
g
(
x
)
[
]
2
2.7 – The Second Derivative, Curvature, and Acceleration
• Terminology
Concave Up
Concave Down
Acceleration
Point of Inflection
Second Derivative
• Find the second derivative of functions
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 Spring '08
 Johnson
 Calculus, Logic, Binomial Theorem, Polynomials, Derivative, Binomial, dx dx dx, Ricker Model Qualitative Dynamical Systems

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