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Appendix B

Table of Derivatives

0
Note: c denotes a constant and denotes differentiation.
d df dg
(fg) = g + f
dx dx dx

0
d f f g − fg 0
=
dx g g 2
d c c−1 0
f = cf f
dx

d 0 0
f(g) = f (g)g
dx

d 2 00 0 2 0 00
f(g) = f (g)(g ) + f g
dx 2

2
n
n
n d
d n n n−1 f dg n−2 f d g d g
n d
n d f
(fg) = g + + + · · · + f
dx n 0 dx n 1 dx n−1 dx 2 dx n−2 dx 2 n dx n
d 1
ln x =
dx |x|
d
x
x
c = c ln c
dx
d df dg
g
g
f = gf g−1 + f ln f
dx dx dx
d
sin x = cos x
dx
d
cos x = − sin x
dx

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