Math Review for Physical Chemistry
Math Review for Physical Chemistry
Math Review for Physical Chemistry
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2<br />
Other trigonometric function definitions<br />
cotθ =<br />
1<br />
tanθ<br />
= cosθ<br />
sinθ<br />
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secθ =<br />
cscθ =<br />
1<br />
cosθ<br />
1<br />
sinθ<br />
€<br />
Trigonometric Identities<br />
sin 2 θ + cos 2 θ = 1<br />
sin2θ = 2sinθ cosθ<br />
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cos2θ = cos 2 θ − sin 2 θ<br />
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II. Calculus [See also <strong>Math</strong>ematical Background 1 and 2 in your text.]<br />
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A. Derivatives<br />
Derivatives of common functions<br />
d<br />
dx x n<br />
= n x n−1<br />
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d<br />
dx eax<br />
= a e ax<br />
d<br />
dx ln x = 1 x<br />
d<br />
sin x = cos x<br />
dx<br />
d<br />
cos x = − sin x<br />
dx<br />
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General rules <strong>for</strong> manipulation of derivatives<br />
d<br />
dx c ⋅ f x<br />
d<br />
dx<br />
d<br />
dx<br />
[ ( )]<br />
= c ⋅ f ʹ′ ( x) (c is a constant)<br />
[ f ( x)<br />
+ g( x)<br />
] =<br />
[ f ( x)<br />
⋅ g( x)<br />
] = f x<br />
d<br />
dx f u x<br />
( ( ))<br />
= df<br />
du ⋅ du<br />
dx<br />
d<br />
dx f x ( ) + d dx g x ( )<br />
( ) ⋅ g ʹ′ ( x) + g( x) ⋅ f ʹ′ ( x) (the Product Rule)<br />
(the Chain Rule)<br />
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