Graphics Reference
In-Depth Information
x
. From qn 42,
f
43 If
f
(
x
)
x
, then
f
(
x
)
is differentiable except at 0.
(
f
(
(
1/(
n
(
f
(
a
)
f
a
))
1/
f
a
)
a
)
)
(1/
n
)
a
.
Now let
P
(
x
)
x
and
Q
(
x
)
x
, then
Q
(
P
(
x
))
x
.
(
Q
P
)
(
x
)
Q
(
P
(
x
))·
P
(
x
)
(1/
q
)(
x
)
px
(
p
/
q
)
x
.
Use qn 17 to extend to negative rational indices.
g
is differentiable at
x
0 provided
r
1.
44 [
,
]
[
1, 1].
sin
(arcsin
x
)· arcsin
x
1, so arcsin
x
1/cos(arcsin
x
)
1/
(1
x
).
45 (
,
). tan
x
(cos
x
sin
x
)/(cos
x
)
1
tan
x
.
tan
(arctan
x
) · arctan
x
1, so arctan
x
1/(1
x
).
46
f
(
x
)
f
(
a
)
x
a
f
:[
a
,
b
]
R is differentiable at
a
if lim
exists and is finite.
Usethelimit from blow for
b
.
