### Ch. 6 Review

```Ch. 6 Review
AP Calculus







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) =

cos
2
, find f’(x).
5 2

1

If g(x) =
, find g’(x).

Example 8, pg. 276
Second Fundamental Theorem of
Calculus
4
8 − 1

3 2
5 − 4 2
tan

Integrating Reciprocal Functions
2 4

2
3 log 2
ln
2

Simplifying Logs

log 5
+2
7

Derivatives of Logs/
Logarithmic Differentiation
Find f’(x) if   =
(3+7)5
3
+2
Derivatives of Logs/
Logarithmic Differentiation
Power Rule, Chain Rule
 Product Rule, Quotient Rule
 e^x
5^x
ln x
log 3

Differentiation/Integration
Methods
= − +
=  +
sec   = ln | sec  + tan | +
csc   = −ln | csc  + cot | +
tan   = ln | sec  | +
cot   = −ln | csc  | +
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) = 0   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
```