Math 1205 solutions Derivatives:
32
2
8
9
23
22 23
2
2
dp
1) Find ,
dq
dp
32
dq
dz
2) Find , z
dy
dz 8
dy
dk
3) Find ,
dh 2
dk 3 ( 2) (1)
dh ( 2)
df( ) sin
4) Find , f( ) tan
dcos
df( )
sec
d
5) Fi
y
y
paq bq
Ans aq bq
ABe
y
A
Ans Be
y
mhp
kh
mhph mhp
Ans h
Ans
θθ
θθ
θθ
θθ
θ
=+
=+
=+
−
=+
=
+
+−
=
+
==
=
2
3
2
dy
nd , tan sec
d
dy
tan sec tan sec sec
d
6) Show that the curve y = 6x 5 3 has no tangent line with slope 4.
dy 1
18 5 4, which is undefined
dx 18
7) An elastic band is hung on a h
y
Ans
x
Ans x x
θθ
θ
θθ θ θ θ
θ
=
=+
+−
−
=+==
ook and a mass is hung on the lower
end of the band. When the mass is pulled downward and then released,
it vibrates vertically. The equation of position of the mass at any time t seconds
is given to
/
be s = 2cos(t) + 3sin(t) centimeters. Find the velocity at t = .
Ans 2sin( ) 3 cos( )sv t t
π
==− +