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Differential calculus - derivatives |
Table
of derivatives of elementary functions |
Differentiation
rules |
Table of derivatives |
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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, |
![](DR.gif) |
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 |
![](DRI.gif) |
Differentiating
parametric equations,
if x = x
(t)
and
y
= y (t)
then |
![](DRP.gif) |
Logarithmic
derivative,
if y
= f
(x)
then,
using the chain rule |
![](DRL.gif) |
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Table
of derivatives of elementary functions |
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c |
0 |
x |
1 |
xn |
nx
n -
1 |
![](D1.gif) |
![](D1A.gif) |
![](D2.gif) |
![](D2A.gif) |
![](D3.gif) |
![](D3A.gif) |
![](D4.gif) |
![](D4A.gif) |
Exponential and logarithmic functions |
![](D7.gif) |
![](D7A.gif) |
![](D8.gif) |
![](D8.gif) |
![](D5.gif) |
![](D5A.gif) |
![](D6.gif) |
![](D6A.gif) |
Trigonometric functions |
![](D9.gif) |
![](D9A.gif) |
![](D10.gif) |
![](D10A.gif) |
![](D11.gif) |
![](D11A.gif) |
![](D12.gif) |
![](D12A.gif) |
Inverse
trigonometric functions |
![](D13.gif) |
![](D13A.gif) |
![](D14.gif) |
![](D14A.gif) |
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![](D15.gif) |
![](D15A.gif) |
![](D16.gif) |
![](D16A.gif) |
Hyperbolic
functions |
![](D17.gif) |
![](D17A.gif) |
![](D17A.gif) |
![](D17.gif) |
![](D18.gif) |
![](D18A.gif) |
![](D19.gif) |
![](D19A.gif) |
Inverse
hyperbolic functions |
![](D20.gif) |
![](D20A.gif) |
![](D21.gif) |
![](D21A.gif) |
![](D22.gif) |
![](D22A.gif) |
![](D23.gif) |
![](D23A.gif) |
Functions
of (x2
±
a2
) |
![](D24.gif) |
![](D24A.gif) |
![](D25.gif) |
![](D25A.gif) |
![](D26.gif) |
![](D26A.gif) |
![](D27.gif) |
![](D27A.gif) |
![](D28.gif) |
![](D28A.gif) |
![](D29.gif) |
![](D29A.gif) |
![](D30.gif) |
![](D30A.gif) |
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