Things
to know
Test 2
for
Derivatives
Limit
Always tidy
·
1. step
/b ]
*
2) Solving y'
=
0
Efficiency
use
:
specific
another
or
3) Before finding
number
f'
y "Lif you found
the basic
↳ basic
rules
as
and
much
rules : const mult rule
now
f")
strig
XL
e*,
,
·
Use
H
(also
needed
limit
for
definition
of
f)
So
·
·
Trig
derivatives
Trig
identities
Trig
values
S[f(x)
*
Sc f(x)dX
.
Sxdx
Se dx
In 1x1
Ssinx dx
*
+
+ =
+
C
,
C , if
(bxdx
-cosX + c
=
Ssec"xdx
tan
=
Ssecxtany dx
=
derivatives
sin X
COSX
tan X
see X
=
ifn
x=
=
1
.
b"
x + c
secx + c
St
*
S dx
Laws
↓
2
logy
dX
of
=
·
tan x
SCOS Xdx
*
log(x)
sinx
+
=
*
cos X
-
cSo2x
.
Cot X
ScSC
*
"
xdX
*
y
y
Y
C
I
=
-
co + X
ScScx0+ Xdx
x
1
-
arccOSX
x2
-
I
X
-
csX
+
I
arccotX-
1 + x2
=
1-
+ C
1 + x2
C
I
X2
I
arccscX
X
arccos(x) =
-
-
XX2
1
=
=
csc(x)
= -arcsec(x)
if
arcsec
log ,
Areas
log ,
log p
Al
:
In (b)
logio(x)
1090 (b)
logy()
-
it
VA
=
y arccoS(x)
=
cos(y)
arc
u-
r
arcsin(x)
= -arctan(x)
log ,
v
-
arccot(x)
u +
(n(x)
=
(sin x) (sinx)
co-functions
Y
=
logs
logy (v/v)
↑
x
(SCX- (Sc X
-
arctan
=
.
logy (ur)
all
In b
arcsec x + C
(u vE
>
-
X0
-
1
arcsinx
=
*
cot X
functions
C
+
secX
X
Sax
for
COS
2
secy
arcsec
*
X
z
- 1
arctan
*
&
=
T
arcsin
*
in(b)
f f(x)dx + (g(x)dX
(mix
=
e +c ;
=
=
c(f(x)dx
=
Econstant
*
Trig
(important
g(x)]dx
+
In
formulas
*
*
e'v(x)
( + important
<- important
Integral
1
I
=
inXfor
Trig
·
=
=
.
Limits
↳ In e
<
[In,x] *
A 4
.
(In b)b
=
[log(x)]
possible
as
+ /-rule ,
,
need
Continuity
·
h
when :
1) Asked
·
:
-
h+ 0
enough)
is
Simplify
·
lim
up
definition
f(x)
+ x)
(n
f
2Trh
HA
lim
X- D
=
X
where
means
O
by I