January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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G
dðu 1 vÞ
dx
5
du
dx
1
dv
dx
G
dðu 2 vÞ
dx
5
du
dx
2
dv
dx
G
dðkuÞ
dx
5 k
du
dx
G
Product rule:
dðu vÞ
dx
5
du
dx
v 1 u
dv
dx
G
Quotient rule:
d
dx
u
v
5
ðdu=dx vÞ2 ðu dv=dxÞ
v
2
G
Chain rule:
y 5 f ðgðxÞÞ; u 5 gðxÞ;
dy
dx
5
dy
du
du
dx
G
Derivative of inverse function:
dy
dx
5
1
dx=dy
where x(y) is the inverse function of y(x).
G
Reciprocal rule:
d
dx
1
y
52
dy=dx
y
2
G
Logarithmic differentiation:
G
y 5 f(x), ln y 5 ln f(x),
G
dy
dx
5 f ðxÞ
d
dx
ln f ðxÞ
½
.
5.4 Table of Derivatives
Independent variable: x
Real constants: C, a, b, c
Natural number: n
G
d
dx
ðCÞ5 0
G
d
dx
ðxÞ5 1
68 Mathematical Formulas for Industrial and Mechanical Engineering
G
d
dx
ðax 1 bÞ5 a
G
d
dx
ðax
2
1 bx 1 cÞ5 ax 1 b
G
d
dx
ðx
n
Þ5 nx
n21
G
d
dx
ðx
2n
Þ52
n
x
n11
G
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.