Given y=f(x) then df/dx is given by
which of the following?
1.
f ( x  h)  f ( x )
h
2.
f ( x )  f ( x  h)
h
3.
f ( x  h)  f ( x )
lim
h 0
h
0%
4
0%
3
0%
2
f ( x )  f ( x  h)
lim
h 0
h
0%
1
4.
cos( 2 x  h)  cos( 2 x)
lim
h 0
h
1.
2.
3.
4.
equals
-2sin2x
-sin(2x)
0
-2xsin2x
0%
1
0%
0%
2
3
0%
4
If y=xn then find dy/dx
nxn
nxn-1
xn-1
(n-1)xn
-1
)x
n
0%
(n
-1
0%
xn
n1
0%
nx
n
0%
nx
1.
2.
3.
4.
Find the derivative of
f(x)=3x³-½x²+5x+1
with respect to x
9x² - 2x + 5
9x³ - x² + 5x + 1
9x² - x + 5
9x³ - x² + 6
0%
4
0%
3
0%
2
0%
1
1.
2.
3.
4.
If
-3e3x
3e3x
-3e2x
-3xe2x
xe
2x
0%
-3
e2
x
0%
-3
3x
0%
3e
e3
x
0%
-3
1.
2.
3.
4.
dy
y  e then find
dx
3x
df
f(k)=tan3k, find
dk
3sec3k
sec3k
3sec²3k
sec²3k
c²
3k
²3
k
ec
3s
c3
0%
se
0%
k
0%
se
ec
3k
0%
3s
1.
2.
3.
4.
d
cos( x) =
dx
1.
2.
3.
4.
5.
sin(x)
-sin(x)
cos(x)
-cos(x)
cosec(x)
0%
1
John Goodband, Coventry University
0%
2
0%
0%
3
4
0%
5
d
dx
 x =
1.
2 x
4.
2
x
2.
1
x
2
3.
1
5.
1
1 .5
2( x )
2 x
0%
1
John Goodband, Coventry University
0%
2
0%
0%
3
4
0%
5
d
ln x =
dx
1.
0%
1
1
x ln x
ln x
John Goodband, Coventry University
0%
0%
0%
0%
5
3.
5.
4
1
x
xln x
3
2.
4.
2
e
x
3
Find the derivative of y  2
x
with respect to x
1.
3
2x
3
4.
0%
0%
0%
4
0%
3
 6x
3
2
6x
6

x
1
3.
2.
Find the derivative of
z = 2sint – cos2t
with respect to t
2cost + sin2t
2cost – sin 2t
2cost + 2sin2t
2cost – 2sin2t
0%
4
0%
3
0%
2
0%
1
1.
2.
3.
4.
If f ( x)  cos x then
1.
f ( x)   f ( x)
2.
f ( x)   f ( x)
3.
f ( x)   sin(x)
4.
0%
4
0%
3
0%
2
0%
1
All of the above
Which of the following statements
are true?
1. The derivatie of
f(x)+g(x) is df  dg
dx
dx
2. The derivative of
f(x)-g(x) is df  dg
dx
dx
3. If k is constant, the
dk
derivative of kf(x) is
dx
4. If y=f(x)g(x) then
dy df
dg

g(x)  f(x)
dx dx
dx
0%
1
0%
0%
2
3
0%
4

d
cos x
2 x  e  sin 2 x
dr
1.
2.
3.
4.
 equals
2-ecosxsinx +2xcos2x
x+ ecosx +2cos2x
2-ecosxsinx +2cos2x
Not enough
information
0%
1
0%
0%
2
3
0%
4
Find the derivative of y=2xe-x
with respect to x
1.
2.
3.
4.
-2xe-x + 2e-x
-2xe-x + 2e-x
2xe-x – 2e-x
2xe-x + 2e-x
0%
1
0%
0%
2
3
0%
4
Find the derivative of y=(e2x)6
with respect to x
6e2x
12e12x
12xex
12ex
ex
0%
12
xe
12
2x
e1
12
0%
x
0%
2x
0%
6e
1.
2.
3.
4.
d
2
sin( x )=
dx
2xcos(x²)
cos(x²)
2xcos(x)
x²cos(x²) + 2xsin(x²)
John Goodband, Coventry University
0%
0%
4
0%
3
1
0%
2
1.
2.
3.
4.
Which of the following is the
quotient rule if y  f ( x) ?
g ( x)
1.
dy df
dg

g ( x) 
f ( x)
dx dx
dx
2.
dy df
dg

g ( x) 
f ( x)
dx dx
dx
df dg

f ( x)
dx dx
g ( x)2
0%
0%
0%
0%
4
dg df
f ( x)

g ( x)
dy
dx dx

dx
g ( x)2
3
4.
2
dy

dx
g ( x)
1
3.
Use the quotient rule to find the
derivative of f(x)=x-3cosx
with respect to x
1.
 x sin x  3 cos x
x4
2.
3 cos x  x sin x
x4
3.
 3x 2 cos x  x 3 sin x
x6
4.
0%
4
0%
3
0%
2
0%
1
3x 2 cos x  x 3 sin x
x6
We know f (2)  2 and f (2)  6 .
d f ( x)
Then
dx x
equals:
x 2
1. 5/2
2. 7/2
3. 3
0%
0%
0%
Using the chain rule, find the
derivative f(x)=(3x²+2)²
with respect to x
2(3x² + 2)
12(3x + 2)
12x(3x² + 2)
12x + 4
0%
x(
3x
12
4
+
x
12
²+
2)
+
(3
x
12
3x
²+
0%
2)
0%
2)
0%
2(
1.
2.
3.
4.
Suppose a runner has a speed of 8 miles per hour, while
a cyclist has a speed of 16 miles per hour. Then dV/dt
for the cyclist is 2 times greater than dV/dt for the runner.
This is explained by:
The chain rule
The product rule
The quotient rule
The addition rule
0%
4
0%
3
0%
2
0%
1
1.
2.
3.
4.
The radius of a balloon changes as it
deflates. This change in radius with
respect to volume is:
1.
dV
dr
3.
2.
dr
dV
dV dr

dr dV
0%
4
0%
3
0%
2
0%
1
4.
None of these
Calculate the second derivative of
y = 4x³ - 2x + x² - 3
with respect to x
24x + 2
24x - 2x
12x - 2
12x² - 2 +2x
+2
x
0%
12
x²
12
-2
x
x
-2
24
x
+
x
0%
-2
0%
2
0%
24
1.
2.
3.
4.
2
d y
then find 2
dx
1.
2 6 1 5 5 4
x  x  x  13 x 2
30
35
12
2.
8 x  x  10x
3
2
3.
24x  2 x  10x  26
2
0%
4.
24x  2 x  10
0%
0%
0%
4
3
2
2
3
1
If
1 3
4
2
y  2 x  x  5 x  26
3
If x=h(t) and y=g(t) then
1.
dy dy dx

dx dt dt
2.
3.
dy dy dx


dx dt dt
dy dy dx


dx dt dt
4.
dy dy dx


dx dt dt
0%
1
0%
2
0%
3
0%
4
Find the valuedyof
if x=3t2 and
dx
y=2t-1.
1.
1
3t
3.
12 t
2.
3t
4.
2  6t
0%
1
0%
2
0%
3
0%
4
If x=h(t) and y=g(t) then
1.
 
 
d y x y y x


2
dx
x3
2
2.
3.
d2y

2
dx
 
 
d y y x x y


2
 
 
dx
3
x
x y y x
2

2
x
4.
 
 
d y y x x y


2
dx
x
2
0%
1
0%
2
0%
3
0%
4
Find the equation of the tangent line

to the curve x=1-3sint, y=2+cost at
t
.
3
1.
y
1
1
x4
3
3
2.
1
y  3x  3 
3
3.
3
3
y
x4
3
3
4.
0%
None of the above
1
0%
2
0%
3
0%
4
Which differentiation rule is needed
to differentiate implicit functions?
1.
2.
3.
4.
Product rule
Chain rule
Quotient rule
Inverse function
rule
0%
1
0%
2
0%
3
0%
4
Find
dy
dx
if 3y=xy+siny.
1.
y
cos y  x  3
2.
3.
y
3  x  cos y
x  y  cos y
3
4.
xy
3 y  sin y
0%
1
0%
2
0%
3
0%
4
Find
d2y
at the point
2
dx 2
x +2xy+y2=x.
1.
2.
1

64
289

256
3.
4.
1

256
289

64
0%
1
(3,1) on
0%
2
0%
3
0%
4