# Ch. 6 Review ```Ch. 6 Review
AP Calculus
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6.2: Integrals of Reciprocal Functions
6.2: Second Fundamental Theorem of
Calculus
6.3: Log Properties (The Big Four)
6.4: Solving Exponential Equations (logs)
6.4: Logarithmic Differentiation
(exponential functions)
Growth/Decay Problems (using logs to
solve)… including Separation of Variables
Derivatives/Integrals of Transcendental
Functions (trig, exponential, logs)
Topics

If f(x) =
𝑥
cos 𝑡
2
𝑑𝑡, find f’(x).
5𝑥 2𝑡
𝑒
1

If g(x) =
𝑑𝑡 , find g’(x).

Example 8, pg. 276
Second Fundamental Theorem of
Calculus
4
8𝑥 − 1
𝑑𝑥
3𝑒 2𝑥
5 − 4𝑒 2𝑥
tan 𝑥
𝑑𝑥
𝑑𝑥
Integrating Reciprocal Functions
2𝑒 𝑙𝑛4𝑥
𝑙𝑛𝑒
𝑥2
3 log 2
ln
𝑥2
𝑠𝑖𝑛𝑥
Simplifying Logs
𝑑
𝑑𝑥
log 5 𝑥
𝑑 𝑥+2
7
𝑑𝑥
Derivatives of Logs/
Logarithmic Differentiation
Find f’(x) if 𝑓 𝑥 =
(3𝑥+7)5
3
𝑥+2
Derivatives of Logs/
Logarithmic Differentiation
Power Rule, Chain Rule
 Product Rule, Quotient Rule
 e^x
5^x
ln x
log 3 𝑥

Differentiation/Integration
Methods
𝑠𝑖𝑛𝑥 𝑑𝑥 = −𝑐𝑜𝑠𝑥 + 𝑐
𝑐𝑜𝑠𝑥 𝑑𝑥 = 𝑠𝑖𝑛𝑥 + 𝑐
sec 𝑥 𝑑𝑥 = ln | sec 𝑥 + tan 𝑥| + 𝑐
csc 𝑥 𝑑𝑥 = −ln | csc 𝑥 + cot 𝑥| + 𝑐
tan 𝑥 𝑑𝑥 = ln | sec 𝑥 | + 𝑐
cot 𝑥 𝑑𝑥 = −ln | csc 𝑥 | + 𝑐
Trig Integrals
See Population Problem, pg. 269.
 We now know how to solve this
QUICKLY!!!

Separation of Variables
Know how to substitute given values into
R(t) = 𝑎0 𝑒 𝑘𝑡 formula.
 Be able to recognize derivative (rate of
change, instantaneous rate, slope of
tangent, etc.) vs. integral (sum, area
under curve, total accumulation).

Exponential Growth/Decay
```