Interactive Real Analysis
- part of
MathCS.org
Next | Previous |
Glossary
|
Map
|
Discussion
Real Analysis
1. Sets and Relations
2. Infinity and Induction
3. Sequences of Numbers
4. Series of Numbers
5. Topology
6. Limits, Continuity, and Differentiation
6.1. Limits
6.2. Continuous Functions
6.3. Discontinuous Functions
6.4. Topology and Continuity
6.5. Differentiable Functions
6.6. A Function Primer
7. The Integral
8. Sequences of Functions
9. Historical Tidbits
Java Tools
Examples 6.5.2(a):
Why these ads ...
Find the derivative of
f(x) = x
and of
f(x) = 1 / x
Back
If
f(x) = x
, then
=
(x - c) / (x - c) = 1
so that
f'(x) = 1
for all
x
.
If
f(x) = 1 / x
, then
=
(1/x - 1/c) / (x - c) = (c - x) / (x - c) * 1 / (x c) = - 1 / c
2
, so that
f'(x) = - 1 / x
2
for all
x
not equal to zero.
Next | Previous |
Glossary
|
Map
|
Discussion