The Official Handy-Dandy Academy Math Cheat Sheet Page 4
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4Newton’s Method Let f be a differentiable function. Assume you have a guess for the root x
where
n
f (x) = 0. Then you get a new guess x
by computing the x-intercept of the tangent line to the graph of
n+1
y = f (x) at the point (x
, f (x
)).
n
n
f (x
)
n
x
= x
−
.
n+1
n
f (x
)
n
A Brief Derivative Table
f
f
r
r−1
x
rx
x
x
a
a
ln(a)
x
x
e
e
1
log
(x)
a
x ln(a)
1
ln(x)
x
sin(x)
cos(x)
cos(x)
− sin(x)
2
tan(x)
sec
(x)
2
cot(x)
− csc
(x)
sec(x)
sec(x) tan(x)
csc(x)
− csc(x) cot(x)
1
arcsin(x)
√
2
1 − x
1
arccos(x)
−
√
2
1 − x
1
arctan(x)
2
1 + x
1
arccot (x)
−
2
1 + x
1
√
arcsec (x)
,
|x| > 1
2
|x|
x
− 1
1
√
arccsc (x)
−
,
|x| > 1
2
|x|
x
− 1
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