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Calc Basic Review
Calc Basic Review
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1
How do you write any point on the unit circle in the coordinate plane? (X, Y)
(Tanø, Cosø)
(Cosø, Tanø)
(Sinø, Cosø)
(Cosø, Sinø)
2
Find the derivative of y = 5
x
1
0
5x
3
what is implicit differentiation?
when y is not a function of x
that cool way to differentiate
differentiation where the function is in explicit form
differentiating using dy/dx inside the equation
4
Select all of the answers that mean the same thing as a DERIVATIVE
prime
slope
Instantaneous rate of change
\frac{Δy}{Δx}
5
Find the derivative
0
pi
DNE
1
6
What is Implicit Differentiation?
when you differentiate terms with respect to x, that aren't x
extreme chain rule
differentiation with respect to x outside of a relationship of x
differentiation for only y
7
Find the derivative of 3sinx - 4cosx.
3cosx - 4sinx
3cosx + 4sinx - 12
3cosx + 4sinx
-3cosx - 4sinx
8
what is sin0?
90
1
∞
0
9
Find the derivative of sin(x)
-cos(x)
sin(x)cos(x)
cos(x)
csc(x)
10
What is cos90
0
?
3
1
0
2
11
What is cos 270
0
3/2
2/3
1
12
Find derivative using product rule
f'(x)=-2cos(x)sin(x)
f'(x)=cos(x)-sin(x)
f'(x)=cos(x)+xsin(x)
f'(x)=cos(x)-xsin(x)
13
What is product rule?
f'(x)g(x) + g'(x)f(x)
f(x)g(x)
f'(x)g'(x) + g'(x)f'(x)
f(x)g(x) + g(x)f(x)
14
True or False: Velocity is the same as Speed.
True
False
15
Find the derivative of cos(x)
csc(x)
tan(x)
-sin(x)
sin(x)
16
What is sin(270
o
)?
1
undefined
-1
0
17
Find the derivative of y = 4cosx
y'=-cos4x
y'=-4sinx
y'=4sinx
y'=cos4x
18
True or False: If velocity and acceleration are negative, then the objects speed is slowing down
True
False
19
Use the power rule to find the derivative.
3x2
3x+6
3x
3x2+6
20
What is the quotient rule of derivatives?
x) / g (x)) ' =( f ' (x) ⋅ g(x) - f (x) ⋅ g ' (x)) / g 2 (x)
(f (x) / g (x)) ' = f ' (x) ⋅ g(x) + f (x) ⋅ g ' (x)
(f (x) / g (x)) ' = f ' (g(x)) / g ' (x)
(f (x) / g (x)) ' = f ' (g(x)) / g ' (x)
21
Use the power rule to find the derivative of y=1/x⁷.
y¹=-7x‐⁸
y¹=-7x⁸
y¹= -7/x‐⁸
y¹=-7/x⁸
22
What is cos0 =
1
0
0.5
sqrt(2)
23
What is the goal of implicit differentiation?
To solve for dy/dx
To solve for y
To solve for x
To find the derivative of x
24
Find the derivative.
f'(x) = -3x
f'(x) = 3x2 - 6x
f'(x) = 0
f'(x) = 3x2 - 6
25
What is calculus?
Study of numbers
Study of lengths and angles
Study of change
Study of mathematical symbols
26
To find velocity from position, you must...
find the 1st derivative
integrate twice
integrate once
find the 2nd derivative
27
What is cos(180°)?
-1
0
Undefined
1
28
What is Sin(180°)?
Undefined
0
1
1/2
29
To find acceleration from velocity, you must...
find the 1st derivative
integrate once
integrate twice
find the 2nd derivative
30
General Power Rule Derivative
n-1nx
nx-1
nxn-1
xn-1
31
Find the derivative of tan(x)
sin(x)/cos(x)
-csc2(x)
sec(x)tan(x)
sec2(x)
32
What is sin90°
undefined
1
-1
0
33
derivative ax
n
axn-1
axn-1 a'
naxn-1
axn+1/n+1
34
True or False: If velocity and acceleration are positive, then the object is speeding up
True
False
