(a)
find
velocity
e
-
-
2(s(t))
X(t)
=
t3
-3
+=
9t
+
1aX(2)
=
3(2):
6(2)
-
9
x
=
3
+
2
-
65
-
9
-12
-
12
-
9
velocity
=
-9
(b)
find
acceleration
&
t
=
2
(S(t)")
X(t)
=
3
+2
-6x
-
9X(2)
=
6(2)
-
6
GX(t)"
=
65
-
6
Garfieration
=
6
sumolangles
>
sin(X+h)=
sinxcosntcosxsinh
&(sinx]=cos
of
(COSx]=-sinx
formulas
cos(Xth)
=
cosXSinh-sinxcos
x
trig
verivation
->
*
(tun):
secx
(corx]
=
-cscx
/im
cOSX-1
=
0
trig
limits
->
Im
sinx=
xeo
x
&
(ecx]
=
secxtanx
&,((S(X]
=
-ascxcotx
2)
Find
derivatives
a
a)
f(x):
sinx)
=
f(x)
=
cosX
(this
is
always
derivative
or
sinx)
b)
f(x)
=
2105(X)
-
6sec(x)
+
3
=-2Sin(X)
-6
tanix)
sec(x)
+
5
afX)=-asinx-bsinx
↑
sinx
(OS(X)2
cosx
=
So
s
1)
f(x)
=
(X
2
+
1)"
a(X
2
1)(X
4))
(X
+
1)
(x4
+
(x
4
+
1)(X2+1)
=
x4
+
x4
+
2x42x7x+1f(x)
=
6x4+12x
+
0x
-
X
*
3x4
3
x
+
o)
f(x)
=
ex's
outer.
"
inner:
x2
&u=
inner
"(ev]
(x]
-
:
2x
f(X)
=
hex
&Y
=
YV.*x
e)
f(x):
tan6X
ranlox)
->
outer:
tanc)Y(tancrs].84
(6x]
f(x)
=
6sec(6x)
"
inner:
6X
4
=
u
-sec.
6
(plugin
us
f)
f(x):
sin
(X41)
->
(sin(xH)
("exponent
Outer:
3
-outside
part
inner:
sin(X")
(U)
=
32
-3/Sin(x2132)
·
2x
(0)
(X)
-
f(X):
6x
SinCX=1)"cos
(x2+1)
->
P!
↳
Y(sin(x)
=
10S(X).2x
outer:
sinu
↓
plit
again)
inner:
XH
⑧!
(sinu).Y(x)
qV=
6
=
r)
=
2X