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Mathematics
11th -
12thgrade
Derivatives - Product and Quotient Rule
41 questions
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- 1. Multiple Choice
What rule should be used in deriving f(x) = x5
Constant rule
Sum rule
Power rule
Difference rule
- 2. Multiple Choice
What rule should be used in deriving h(x) = 2(x - 4)3
Power rule
Product rule
Quotient rule
Chain rule
- 3. Multiple Choice
What is the derivative of f(x) = 2x3 - 4x + 5?
f'(x) = 6x2 - 4x
f'(x) = 2/3x2 - 4x
f'(x) = 3x2 - 4
f'(x) = 6x2 - 4
- 4. Multiple Choice
Which function has the derivative of g'(x) = 4x3 + 2x - 1
g(x) = 2x4 + 2x2 - 1
g(x) = x4 + x2 - x
g(x) = 2x3 + x3 - 2x
g(x) = x5 + x2 - x
- 5. Multiple Choice
Choose the best rule to derive the function.
Product rule
Quotient rule
Power rule
Chain rule
- 6. Multiple Choice
At which point(s) will the slopes of the tangent line are zero?
at C only
at points A, C and E only
at point B and D only
at points A and E only
- 7. Multiple Choice
Let y = (x - 1)(x + 2). Find dy/dx.
2x + 1
2x - 1
4x - 1
2x2 + x - 1
- 8. Multiple Choice
Let f(x) = (x - 1)(x + 2). Find f'(0)
0
1
2
3
- 9. Multiple Choice
Given f(x) = ax2 + 2bx. What are a and b if f'(x) = 8x + 6?
a = 2 and b = 3
a = 3 and b = 2
a = 3 and b = 4
a = 4 and b = 3
- 10. Multiple Choice
At what point will the slope of y = -x2 + 4 is zero?
(0, 4)
(1, 4)
(4, 0)
(1, 0)
- 11. Multiple Choice
What is the slope of the line normal to the curve y = x2 + x at x = 1?
-1
-1/2
-1/3
-1/4
- 12. Multiple Choice
What is the equation of the line tangent to the curve y = x2 at x = 1?
y = 2x + 1
y = 2x - 1
y = -2x + 1
y = x - 1
- 13. Multiple Choice
What is the derivative of f?
1/(x - 1)-1
-1/(x - 1)-2
-1/(x - 1)
-1/(x - 1)2
- 14. Multiple Choice
Let y = x3 - 3x. At what value of x will the rate of change is zero? Choose the best answer.
at x = 0 only
at x = -1 only
at x = 1 only
at x = -1 or x = 1 only
- 15. Multiple Choice
What is the equation of the line tangent to the curve y = -x2 + 3 at (1, 2)?
y = 2x - 4
y = -2x - 4
y = -2x + 4
y = 2x + 4
- 16. Multiple Choice
What is the derivative of y = 2π?
0
2
-2
None of the above
- 17. Multiple Choice
What is the rate of change of f(t) = 2t3 - 4t + 1 when t = 2s and f is in meter (m)?
16 m/s
20 m/s
24 m/s
30 m/s
- 18. Multiple Choice
What is the 2nd derivative of y = 2x3 - 4x + 6
6x2 - 4
12x - 4
12x
6x
- 19. Multiple Choice
Let f(x) = 2x - 1 and g(x) = x2. If y = f[g(x)], then what is y’?
2x
4x
2x - 1
2(2x - 1)
- 20. Multiple Choice
if f(x) = x2 + 3, then f’’(0) is
0
2
4
Undefined
- 21. Multiple ChoiceWhat is the derivative of xn?(n-1)xnnxn+1(n+1)xn-1nxn-1
- 22. Multiple ChoiceFind the derivative of the given equation
f(x) = 7707x14 - 23. Multiple ChoiceFind the derivative of the given equation
f(x) = -4x4x-40 - 24. Multiple ChoiceFind the derivative of the given equation
f(x) = 1 - x21 - 2x-2x-2-1 - 25. Multiple ChoiceFind the derivative of the given equation
f(x) = x3 + x2 + 33x2 + 2x3x + 2x3x + 2x + 3x3 + x2 - 26. Multiple Choicefindy = 2 x-1y=2 x-2y= −2x-2y= −2 x-1
- 27. Multiple ChoiceSet up the derivative of y=(3x4 - 7)*(5x2 + 1)(12x3)*(10x)(3x4 - 7)*(10x) + (12x3)*(5x2 + 1)(3x4 - 7)*(10x) - (12x3)*(5x2 + 1)(3x4 - 7)/(10x) + (12x3)/(5x2 + 1)
- 28. Multiple ChoiceWhat is the derivative of sin(x)?-sin(x)-cos(x)cos(x)sin(x)
- 29. Multiple ChoiceWhat is the derivative of cos(x)?sin(x)-sin(x)cos(x)-cos(x)
- 30. Multiple ChoiceWhat is the derivative of tan(x)?-sec2(x)-csc2(x)sec2(x)csc2(x)
- 31. Multiple ChoiceWhat is the derivative of sec(x)?sec(x)tan(x)csc(x)cot(x)-sec(x)tan(x)-csc(x)cot(x)
- 32. Multiple Choice
Which of the following is the derivative of g(x)= (x2)(2x4 + 2)5 ?
g'(x)= (2x)(2x4 + 2) 5 + (x2)(5(2x4 + 2)4(8x3))
g'(x)= 2x + 8x3
g'(x)= (2x)(2x4 + 2)5 + (x2)(8x3)
g'(x)= (2x)(5(2x4 + 2)5(8x3)) + (x2)(2x4 + 2)
- 33. Multiple Choice
Which of the following is the quotient rule for derivatives?
h'(x)=((g(x)f'(x) + f(x)g'(x)) / (g(x))2
h'(x)=((g'(x)f'(x) - f(x)g(x)) / (g(x))
h'(x)=((g(x)f'(x) - f(x)g'(x)) / (g(x))2
h'(x)=((g'(x)f'(x) + f(x)g(x)) / (g(x))
- 34. Multiple Choice
Which of the following is the derivative of the function h(x)= (8x6 + 2x + 5)4 ?
h'(x)= 4(8x6 + 2x + 5)3(48x5 + 2)
h'(x)= 4(48x5 + 2)3
h'(x)= 4(48x5 + 2 + 5)3
h'(x)= 3(8x6 + 2x + 5)4(48x5 + 2)2
- 35. Multiple Choice
Which of the following is the chain rule for derivatives utilizing the original function h(x) = f(g(x))
h'(x)=(f'(g(x))(f'(x))
h'(x)=(f'(g(x))(g(x))
h'(x)=(f'(g(x))(f(x))
h'(x)=(f'(g(x))(g'(x))
- 36. Multiple Choice
Which of the following is the derivative of the function h(t) = t4 - (t4 - 1)8 ?
h'(t)= 4t3 - 8t3(t4 - 1)8
h'(t)= 4t3 - 32t3(t4 - 1)7
h'(t)= 4t3 - 8(t4 - 1)7
h'(t)= 4t2 - 32t3(t4 - 1)8
- 37. Multiple ChoiceWhat is f'(x) if f(x) = cos(5x4)?f'(x) = sin(20x3)f'(x) = 20x3 sin(5x4)f'(x) = -sin(20x3)f'(x) = -20x3 sin(5x4)
- 38. Multiple Choice
Find an equation of the tangent line to the graph of f(x) at the point (1, 100), Refer to page 139, example 12.
f(x) = (5x5 + 5)2
y = 500x + 400
y = 100x + 400
y = -500 x - 400
y = 500x - 400
- 39. Multiple Choice
Which of the following is the product rule for derivatives utilizing the original function h(x) = f(x)g(x) ?
h'(x)= f'(x)g'(x)
h'(x)=f'(x)g'(x) + f(x)g(x)
h'(x)=f'(x)g(x) - f(x)g'(x)
h'(x)=f'(x)g(x) + f(x)g'(x)
- 40. Multiple Choice
Let f(x) = (x - 1)(x + 2). Find f'(0)
0
1
2
3
- 41. Multiple Choice
What is the equation of the line tangent to the curve y = -x2 + 3 at (1, 2)? Refer to page 139, example 12
y = 2x - 4
y = -2x - 4
y = -2x + 4
y = 2x + 4
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