Calculus
Name:
Find the derivative of the given function.
L y=*'-!*'*!*
'84
2.
4.y=Ji*t*I
5.r=sec(l
.lx
7.y=ln{¿+"')
10. s=log,(r-z)
13.
f
y=¡sse-r,-!n,
"2
rnd
16.
(l
ax
y'
y=2sinxcosx
3. s=cos(t-zr)
+3d)
6.y=xzcsclx
8.y=¿(r*r"Ð
11. y=.¡çr''
9.r=hþos-';)
14. y=2s6s-r
15. y=sse-r(...r)
72.
"-^lll7
y=¿Á"
for the following.
=t-?x
17.
y'
+
y =2cosx
Find an equation for the (a) tangent and O) normal to the curve at the indicated point.
18. y = "[x' -2x, x
19. x' +2y' =9, Q,Z)
=3
20. Find an equation for the line tangent to the curve x = 3cosl, y = 4sint at the point
defined bv
t=?L.
21. On Earth,
the paper clip
4
if you shoot a paper clip 64 ft straight up into the air with a rubber band,
will be s(r) = 64t -16t2 feet above your hand at / sec after fîring.
ta)
un¿
\-' Find
- ---- 4t ----
dt
4: '
dt'
(b) How long does it take the paper clip to reach its maximum height?
(c) With what velocity does it leave your hand?
(d) On the moon, the same force
s(u)= 64t
will
send the paper
clip to a height of
-2.øt' ft in I sec. About how long will it take the paper clip to reach its
maximum height, and how high will it go?
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319.