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Given y=f(x) then df/dx is given by which of the following?. 1 2 3 4. 1. 2. 3. 4. equals. -2sin2x -sin(2x) 0 -2xsin2x. If y=x n then find dy/dx. nx n nx n-1 x n-1 (n-1)x n. Find the derivative of f(x)=3x³-½x²+5x+1 with respect to x. 9x² - 2x + 5 9x³ - x² + 5x + 1 - PowerPoint PPT Presentation
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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.
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