1. Differentiate exponential
Functions

2. f(x) = 2x
slope ­ always positive f ' is positive
­ increasing increasing

3. Calculate the derivative of f(x) = bx
f '(x) = lim f(x + h) ­ f(x)
h 0
h
x + h
lim b ­ bx
= h 0
h

4. lim bx . bh ­ bx
= h 0
h
lim bh ­ 1
x
= b
h 0
h
=b x
lim bh ­ 1
h 0
h

5. lim bh ­ 1
h 0
h

6. f(x) = 2x
f '(x) = ln2 (2x)

7. f(x) = 3x
f '(x) = ln3 (3x)

8. Find the derivative of f(x) = ex
d (ex)
= ln e (ex)
dx
= ex
f '(x) = ex

9. .
Given f(x) = 3 4x + 7ex
find d (f(x))
dx

10. Exercise 4.2
odd questions
1 ­ 21