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36 questions
h→0lim(h5(x+h)2−5x2)
5x2
10x
10
DNE
Given y=vu , what is y′ ?
(vu' - uv')/v2
(uv' - vu')/v2
(vu' - uv')/u2
(uv' - vu')/u2
What is the average rate of change of f(x) = x2 on the interval [1,3]?
8
10
4
5
What is the instantaneous rate of change of f(x) = x2 at x = 3?
2x
3
9
6
Write the slope of the line tangent to the graph of the function below at the point x = 8.
y=x2−22
-4
-8
16
This is the equation of the line tangent to the graph of the function below at the point (-1, 4).
y=x2+3y = -2x + 2
y = 2x + 2
-(1/2)x + (7/2)
y = (1/2)x + (7/2)
Which option is using correctly the quotient rule?
Differentiate y=x212 .
24x-1
-24x-3
-24x-1
6x-3
Which of the following represents the derivative of a function?
f'(x)
y'
dy/dx
all of the above
Given y=u⋅v , find dxdy .
u'v - uv'
uv' - vu'
u'v + v'u
v'u' + vu
Let y = (x - 1)(x + 2). Find dy/dx.
2x + 1
2x - 1
4x - 1
2x2 + x - 1
What is the derivative of f?
1/(x - 1)-1
-1/(x - 1)-2
-1/(x - 1)
-1/(x - 1)2
dxdx3cosx=
−3x2sinx
x3sinx+3x2cosx
−x3sinx+3x2cosx
3x2sinx+x3cosx
Find the derivative of y= -2cos x + 4sin x
y' = -2sin x + 4cos x
y' = -2sin x - 4cos x
y' = 2sin x + 4cos x
y' = 2sin x - 4cos x
Differentiate:
dxdy=sin2x2xsinx−x2cosx
dxdy=sin2x2xsinx+x2cosx
dxdy=sin2x2sinx−x2cosx
dxdy=sin2x2xsinx−cosx
Find the equation of the tangent line at the point (-1,1) of: f(x) = x4
y=−41x−3
y=−4x−3
y=41x+3
y=4x+3
Find the derivative of
f(x)=xex
f′(x)=ex
f′(x)=2xex
f′(x)=ex−xex
f′(x)=ex+xex
What is the derivative of y = 2π?
0
2
-2
None of the above
You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If h(x)=f(x)−g(x) Find h′(4)
23
2−3
2−1
−3
You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If h(x)=f(x).g(x) Find h′(1)
23
2
2−1
−3
For what value(s) of x is the function continuous but not differentiable?
x = -1
x = 0
x = 2
x = 3; x = -2
Graph of a function is given.Where is the function continuous yet NOT differentiable?
x = a, b, c, d
x = b, c, d
x = a, b,
x = b, d
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