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Derivatives and Nonsense
Derivatives and Nonsense
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1
What is the derivative of a constant?
The value decreases by 2
The value remains the same
The value increases by 4
The value becomes 0
2
Find the derivative of (x
4
+ 3x)
-1
x4 + 3x
-(x4 + 3x)-2(4x3 + 3)
-(x4 + 3x)(4x3)
-x4 + 3x + 4x3
3
Find the derivative of .5x + 72x^2
72x + .5x
144x + .5
.5 + 72x
144 + .5x
4
What is the first step that one should take in order to find the derivative of 2x^6
Add the value of the coefficient and the exponent
Decrease the value of the exponent by 2
Divide the coefficient by the value of the exponent
Multiply the coefficient by the value of the exponent
5
Find the derivative of 5x
7
+ 64
2
- 16x
35x6 + 64x2 + 16
35x6 + 128x -16
35x6 + 64x2 + 16
35x6 + 128x
6
Find dy/dx of 6x
3
- 9x + 4
-9 + 6x3
6x2 + 9
18x2 + 4
18x2 - 9
7
Which rule states that the entire function must be multiplied by the value INSIDE the "bubble?"
Multiplication Rule
Product Rule
Chain Rule
Fundamental Theorem of Calculus
8
Max and Mins occur where the derivative equals.....
x
1
0
DNE
9
When using l'Hospital's Rule, take the ________ of the numerator and denominator.
Quotient Rule
Simplified Function
Derivatives
Quotient
10
Which method would easily take the derivative of the function f(x)=x
3
y
2
Fundamental Theorem of Algebra
Product Rule
Division Method
Quotient Rule
11
Find the derivative of cos(x)
-sin(x)
-cos(x)
cos(x)
sin(x)
12
Find the derivative of e
x
(sinx)
ex(sinx) + cosx
xe(cosx)
ex(sinx)
ex(cosx) + ex(sinx)
13
Find the second derivative of the function x
3
+ 2x
2
+ 8
3x2 + 4x
6x + 2x2
6x
6x + 4
14
Find the derivative of 4x
8
+ 64x
2
+ 13
32x7 + 128
128x + 32x2
128x2 + 8x2
32x7 + 128x
15
Which method is used to find the derivative of (8x
4
+ 3x)/(7x
3
- 4x
2
)?
Multiplication Rule
Dividend Theorem
Quotient Rule
Implicit Differentiation
16
During which process is it necessary to include ( + C) at the end?
When finding dy/dx
When taking the antiderivative
When calculating velocity
When taking the second derivative
17
What cannot be found by using derivatives?
Volume
Inflection Points
Velocity
Maximums
18
Find the derivative of the function: 3x
3
+ 18x
2
+ 4
9x^2 + 36
18x + 4 + 9x^2
9x^2 + 36x
9x^2 + 18
19
What can be found using the second derivative of a function?
Acceleration
Inflection Points
Position
Velocity
20
Which of the following can be found by using the FIRST derivative?
Velocity
Position
Acceleration
Points of Inflection
21
Find the first derivative of the function (6x
2
+7x)
4
4(6x2 + 7x)3(12x + 7)
(6x2 + 7x)4
4(6x2 + 7x)
4(6x2 + 7x)3
