1. Differentiation of Exponential Functions
Problem:
Differentiate f(x) = 10x from first principles.
f’(x) =
lim
h->0
f(x + h) – f(x) h =
lim
h->0
10x+h – 10x h
Use your calculator to evaluate limit.
Try h=0.0001 =
lim
h->0
10x x (10h – 1) h =
lim
h->0
(10h – 1) h
10x x =
10x x

2. Differentiation of Exponential Functions
Problem:
Differentiate f(x) = 2x from first principles.
f’(x) =
lim
h->0
f(x + h) – f(x) h =
lim
h->0
2x+h – 2x h
Use your calculator to evaluate limit.
Try h=0.0001 =
lim
h->0
2x x (2h – 1) h =
lim
h->0
(2h – 1) h
2x x =
2x x

3. Differentiation of Exponential Functions
Problem:
Differentiate f(x) = 2.7x from first principles.
f’(x) =
lim
h->0
f(x + h) – f(x) h =
lim
h->0
2.7x+h – 2.7x h
Try h=0.0001
Use your calculator to evaluate limit. =
lim
h->0
2.7x x (2.7h – 1) h =
lim
h->0
(2.7h – 1) h
2.7x x =
2.7x x

4. Differentiation of Exponential Functions
Problem:
Differentiate f(x) = ex from first principles.
f’(x) =
lim
h->0
f(x + h) – f(x) h =
lim
h->0
ex+h – ex h
Use your calculator to evaluate limit.
Try h=0.0001 =
lim
h->0
ex x (eh – 1) h =
lim
h->0
(eh – 1) h
ex x
= ex x

5. Differentiation of Exponential Functions
Problem:
Differentiate f(x) = nex from first principles.
f’(x) =
lim
h->0
f(x + h) – f(x) h =
lim
h->0
nex+h – nex h
Try h=0.0001
Use your calculator to evaluate limit. =
lim
h->0
nex x (eh – 1) h =
lim
h->0
(eh – 1) h
nex x =
nex =
nex x