|
|
|
|
Differential calculus - derivatives |
Table
of derivatives of elementary functions |
|
Differentiation
rules |
|
Table of derivatives |
|
|
|
|
|
|
| Table
of derivatives of elementary functions |
| Differentiation
rules |
| If
u
= f (x) and
v = g (x)
are differentiable functions and c
is a real constant then, |
 |
| Chain
rule
6)
[
f (g (x))]′ = f ′
(g
(x)) ·
g
′ (x) |
| Differentiating
inverse function, since
f
[ f -1
(x)] = x
then,
using the chain rule |
 |
| Differentiating
parametric equations,
if x = x
(t)
and
y
= y (t)
then |
 |
| Logarithmic
derivative,
if y
= f
(x)
then,
using the chain rule |
 |
| |
| Table
of derivatives of elementary functions |
|
|
|
| c |
0 |
| x |
1 |
| xn |
nx
n -
1 |
 |
 |
 |
 |
 |
 |
 |
 |
|
Exponential and logarithmic functions |
 |
 |
 |
|
 |
 |
 |
 |
| Trigonometric functions |
 |
 |
 |
 |
 |
 |
 |
 |
| Inverse
trigonometric functions |
 |
 |
 |
 |
|
|
|
|
 |
 |
 |
 |
| Hyperbolic
functions |
 |
 |
|
|
 |
 |
 |
 |
| Inverse
hyperbolic functions |
 |
 |
 |
 |
 |
 |
 |
 |
| Functions
of (x2
±
a2
) |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
|
