,)* ,)T

OIFT
DERIVATIVES OF INVERSE FUNCTIONS
by Tom Reardon
1-
Let g(x) = x5 + 3x
-2, and let g-1 denote the inverse of g. Then (g-')'(z)
qr= S>q+3
x5+jx*2, 2 Xti3.-4=O ,gt(,):gyuq3
iz I
D)8
E) 83
c)1
A)1
'83
@*
Let
,1 -\_.'
;X" +* x
f
(x\ =
rrt
A
A)'31
-:
-*- t')-
y!+*x
{=z
-- 3
X3 +t+X-t(o = O
,()+.t^-'t0--tJ
the!.gf-f . The n
- 1, and let r I denote thF-invers€
fyl*t
{4)4
t({:4x'+t
-F'(r)=4&) +r =e
B)1
,6
3. Let f(x)
f,n9)
f'Q),
A)
81
4.
Let h(x)
@+
= xu +x. Find the value of
=
{xt+l
5l{
x3 + 2x
and let
+.}x --1,) l=(
a-=
-6= x3
aj+Z* -3
B)5
A)14
5. lt f(4): 5 and f'(4) =
A)1
,5
6. tf
s(k}
o)x
f
,
h-1
and s'(3) =
,na
o
f,
,)*
at x = 2.
(f')'(s)
yT+V-z
KLt
c)
=
ct
o*
E)-*
denote the inverse of h. Then
(n')'(z)
3>z +z
hl(I)=
h'Lt )= >
.'r'14
1
D)1
,9
@t
E)4
3
4'
6
5
0t
is equal to:
,)T
tf,"n calculate: (f-')'tS).
C\?
,3
E
dx
0*
B)1
,4
B):
lft(n
c)1
'81
B)6
:
is equal to:
Er1
,7
is equal to:
j>ri+y_z__O
7. Let ,@r;-rl)i,i,^iJ'F:rn-,)b=" t1iiX"f1s9,r;nction
o);
8.
Let
o1
'11
1
11
f(x) = xs + 1 and let g
or
r'
what is the varue ot s'(2)?
-1
or1
'13
be the inverse fu.nction of
Er'13
f.
What is the value of g'(0)?
c-*t+t 6x,-t {'$6xa \r(-).i
D) g'(0) does not exist
c)1
A\ -1
E) g'(0) cannot be determined from the given information
g. The following table shows the values of differentiable functions
x
f
f'
g
g'
1
2
1
-3
5
0
2
3
4
2,
2.
3
1r
3
4
o
2
4
4
f
and
g-
3
1
2
lf H(x) = f-'(x), then H'(3) equals
-1
B),8-1
A)'16
")
D)1
,2
-;
10. The following table shows the values of differentiable functions
g
g'
f'
f
x
6
1
-1
-2
-1
2
01 -1
2
(-1
Y
4
3
4
7
1
2
3
B)0
C) undefined
f
and
g.
5
4
3
lf H(x) = f-'(x), then H'(1) equals
A)1
o', +
o);
-L
@1-r
.F\ 4
,?tl
b=xj'
11. Let f(x) =
&
f
f -!';"let
x
B\
$rd = 3*""
x'- L
1
r
denote the invers e ot
*rt
/= {/-,.t
12. Let h(x) =
Jx4
A\!
,4
B)1
,8
(-')'9
r
is equal to:
g)-1
-{}
12
A'Pr'\
IrxXt-,r)
and let
h-1
1T
denote the inverse of h. Then
(r,")'(2) is equal to:
->
4
1
E),2-
'17
-<x<22
"t r'[;),
let
g
be the inverse function of
t,
w
^^Y
f.
What is the value
l'(€\=
$/= cos64
(s>Vt)' 9€i
@
'lz
a9
D)2
L
7T
bxLzt
xL+t
1r3{u\-A rt
s(e|
lL=axi'x*
-11x1 atx=
g(x) = 2x3 - x2 +1. Find the value of
fi0
3
-_
q*
= _3,
A)1
,4
Then
c)8
13. Let f( x) = sinx
14. Let
f.
D\
:__L
c)1
'12
1
,6
{tz), \z +
b
h,(2)
,)*
Tom Reardon tnverce Gifts,
1
3
13.
.
Compute
.'
(h')
D)3
{u
(-3)
'>rt-rl
2-O
.L
ts,t
'
D)20
c)13
h'(-3)
a'Cz) =
U
,,
1
5
-L
ft
E)
1
-5
tnc. http://www.tomreardon.com/Deriv-Inverse-Gift'doc

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