Calculus Final: Chapter 3 (Derivatives) Flashcards

1

Chain Rule

4(x-5)5-1
20((x+5)5-1)3 (x+5)4
5(x+5)4
4((x+5)5-1)3

2

Higher Order Derivative

99
0
x99
100

3

Solve using the product rule

(x2-2)(-x-2)
4x+2x-2+1
(2x)(-1x-2)
2x2-1x-1-4

4

Chain Rule

5x2+3
4(5x2+3)3
40x(5x^2+3)7
40x(5x2+3)3

5

Chain Rule with Exponentials

3e2x^2
e6x
e2x × e3
6x2e2x^3

6

Higher Order Derivative

8000x16
4x6/6- 5x5/5
4x4-5x3
20x4 - 20x3

7

Product Rule

-2x6+2x4-3x2-3
16x10-48x6+2x5-6x
16x4
18x10-48x6+2x5-6x

8

Which of the following does not have a specific rule for solving the derivative?

Divide
Multiplication
Composite Function
Addition/Subtraction

9

Chain Rule with Logarithms and Trig

-sin(ln(4x3))(12x2)/4x3
3(cos(ln(4x))
sinln4x3
3(cos(ln(4x))2

10

What is the slope of a tangent line?

Undefined
0
1
Derivative

11

Solve using the quotient rule

-7/(3x+1)2
3x-x+2
(3x+1)2/-7
(-1)(3x+1)

12

Quotient Rule

(-2x7+3x6+15x4+9x2-6x)/ (x10+6x5+9)
x10+6x5+9
-2x7+3x6+15x4+9x2-6x
(x10+6x5+9)/ (-2x7+3x6+15x4+9x2-6x)

13

Quotient Rule

(12x8-12x5+100x4+20x)
(12x8-12x5+100x4+20x)∕(9x8+30x4+25)
x+2x+5
(9x8+30x4+25)

14

Quotient Rule

2
0
x2
x+1

15

Solve using quotient rule

x / (1-x2)1/2
1 /√(1-x2)3
√(1-x2)3
1/2 (1-x2)-1/2

Calculus Final: Chapter 3 (Derivatives)

Questions 15

Calculus Final: Chapter 3 (Derivatives)

Questions 15