Given y=f(x) then df/dx is given by which of the following?

1 2 3 4

0% 0%0%0%

h

xfhxf )()( 1.

h

hxfxf )()( 2.

h

xfhxfh

)()(lim

0

3.

h

hxfxfh

)()(lim

0

4.

equals

1 2 3 4

0% 0%0%0%

h

xhxh

)2cos()2cos(lim

0

1. -2sin2x

2. -sin(2x)

3. 0

4. -2xsin2x

If y=xn then find dy/dx

nxn

nxn

-1 x

n-1

(n-1

)xn

0% 0%0%0%

1. nxn

2. nxn-1

3. xn-1

4. (n-1)xn

Find the derivative of f(x)=3x³-½x²+5x+1with respect to x

1 2 3 4

0% 0%0%0%

1. 9x² - 2x + 5

2. 9x³ - x² + 5x + 1

3. 9x² - x + 5

4. 9x³ - x² + 6

If

-3e3

x 3

e3x

-3e2

x

-3xe

2x

0% 0%0%0%

dx

dy findthen 3xey

1. -3e3x

2. 3e3x

3. -3e2x

4. -3xe2x

f(k)=tan3k, find

3se

c3k

sec

3k

3se

c²3k

sec

²3k

0% 0%0%0%

1. 3sec3k

2. sec3k

3. 3sec²3k

4. sec²3k

dk

df

=

1 2 3 4 5

0% 0% 0%0%0%

)cos(xdx

d

1. sin(x)

2. -sin(x)

3. cos(x)

4. -cos(x)

5. cosec(x)

John Goodband, Coventry University

=

1 2 3 4 5

0% 0% 0%0%0%

xdx

d

John Goodband, Coventry University

x21.

x2

12.

x2

13.

x

24.

5.1)(2

1

x

5.

=

1 2 3 4 5

0% 0% 0%0%0%

xdx

dln

John Goodband, Coventry University

xe1.

x

12.

xx ln

13.

xx ln4.

xln5.

Find the derivative of

1 2 3 4

0% 0%0%0%

2

3

xy

x2

31.

x

6

2.

36 x3.

36 x4.

with respect to x

Find the derivative of z = 2sint – cos2twith respect to t

1 2 3 4

0% 0%0%0%

1. 2cost + sin2t

2. 2cost – sin 2t

3. 2cost + 2sin2t

4. 2cost – 2sin2t

If then

1 2 3 4

0% 0%0%0%

xxf cos)(

)()( xfxf 1.

)()( xfxf 2.

)sin()( xxf 3.

All of the above4.

1. The derivatie of f(x)+g(x) is

2. The derivative of f(x)-g(x) is

3. If k is constant, the derivative of kf(x) is

4. If y=f(x)g(x) then

Which of the following statements are true?

1 2 3 4

0% 0%0%0%

dx

dg

dx

df

dx

dg

dx

df

dx

dk

dx

dgf(x)g(x)

dx

df

dx

dy

equals

1 2 3 4

0% 0%0%0%

xexdr

d x 2sin2 cos

1. 2-ecosxsinx +2xcos2x

2. x+ ecosx +2cos2x

3. 2-ecosxsinx +2cos2x

4. Not enough information

Find the derivative of y=2xe-x

with respect to x

1 2 3 4

0% 0%0%0%

1. -2xe-x + 2e-x

2. -2xe-x + 2e-x

3. 2xe-x – 2e-x

4. 2xe-x + 2e-x

Find the derivative of y=(e2x)6

with respect to x

6e2

x

12e

12x

12x

ex 1

2ex

0% 0%0%0%

1. 6e2x

2. 12e12x

3. 12xex

4. 12ex

=

1 2 3 4

0% 0%0%0%

)sin( 2xdx

d

John Goodband, Coventry University

1. 2xcos(x²)

2. cos(x²)

3. 2xcos(x)

4. x²cos(x²) + 2xsin(x²)

Which of the following is the quotient rule if ?

1 2 3 4

0% 0%0%0%

)(

)(

xg

xfy

)()( xfdx

dgxg

dx

df

dx

dy

1.

)()( xfdx

dgxg

dx

df

dx

dy

2.

2)(

)()(

xg

xfdxdg

dxdf

xg

dx

dy

3.

2)(

)()(

xg

xgdxdf

dxdg

xf

dx

dy

4.

Use the quotient rule to find the derivative of f(x)=x-3cosx

with respect to x

1 2 3 4

0% 0%0%0%

4

cos3sin

x

xxx 1.

4

sincos3

x

xxx 2.

6

32 sincos3

x

xxxx 3.

6

32 sincos3

x

xxxx 4.

We know and .

Then equals:

1 2 3

0% 0%0%

2)2( f 6)2( f

2

)(

xx

xf

dx

d

1. 5/2

2. 7/2

3. 3

Using the chain rule, find the derivative f(x)=(3x²+2)²

with respect to x

2(3

x² +

2)

12(

3x +

2)

12x

(3x²

+ 2

)

12x

+ 4

0% 0%0%0%

1. 2(3x² + 2)

2. 12(3x + 2)

3. 12x(3x² + 2)

4. 12x + 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:

0% 0%0%0%

1. The chain rule

2. The product rule

3. The quotient rule

4. The addition rule

The radius of a balloon changes as it deflates. This change in radius with

respect to volume is:

0% 0%0%0%

dr

dV1.

dV

dr2.

dV

dr

dr

dV

3.

None of these4.

Calculate the second derivative ofy = 4x³ - 2x + x² - 3with respect to x

24x

+ 2

24x

- 2x

12x

- 2

12x

² - 2

+2x

0% 0%0%0%

1. 24x + 2

2. 24x - 2x

3. 12x - 2

4. 12x² - 2 +2x

If then find

1 2 3 4

0% 0%0%0%

2653

12 234 xxxy

2

2

dx

yd

2456 1312

5

35

1

30

2xxxx

1.

xxx 108 23 2.

2610224 23 xxx3.

10224 2 xx4.

If x=h(t) and y=g(t) then

1 2 3 4

0% 0%0%0%

dt

dx

dt

dy

dx

dy

1.

dt

dx

dt

dy

dx

dy

2.

dt

dx

dt

dy

dx

dy

3.

dt

dx

dt

dy

dx

dy

4.

Find the value of if x=3t2 and y=2t-1.

1 2 3 4

0% 0%0%0%

dx

dy

t3

11.

t32.

t123.

t62 4.

32

2

x

xyyx

dx

yd

1.

If x=h(t) and y=g(t) then

1 2 3 4

0% 0%0%0%

32

2

x

yxxy

dx

yd

2.

22

2

x

xyyx

dx

yd

3.

x

yxxy

dx

yd2

2

4.

Find the equation of the tangent line to the curve x=1-3sint, y=2+cost at

.

1 2 3 4

0% 0%0%0%

3

t

3

14

3

1 xy

1.

3

133 xy

2.

3

34

3

3 xy

3.

None of the above4.

Which differentiation rule is needed to differentiate implicit functions?

1 2 3 4

0% 0%0%0%

1. Product rule

2. Chain rule

3. Quotient rule

4. Inverse function rule

Find if 3y=xy+siny.

1 2 3 4

0% 0%0%0%

dx

dy

3cos xy

y1.

3

cos yyx 2.

yx

y

cos3

3.

yy

xy

sin3

4.

Find at the point (3,1) on x2+2xy+y2=x.

1 2 3 4

0% 0%0%0%

2

2

dx

yd

64

1

1.1.

256

289

2.2.

256

1

3.3.

64

289

4.4.