Calculus
1.What is the derivative of f(x) = 3x^2 – 4x + 1?
a) f'(x) = 6x – 4
b) f'(x) = 6x – 4x + 1
c) f'(x) = 3x – 4
Answer: a) f'(x) = 6x – 4
2. What is the derivative of f(x) = sin(x)?
a) f'(x) = cos(x)
b) f'(x) = -sin(x)
c) f'(x) = tan(x)
Answer: a) f'(x) = cos(x)
3. What is the derivative of f(x) = ln(x)?
a) f'(x) = 1/x
b) f'(x) = x
c) f'(x) = 0
Answer: a) f'(x) = 1/x
4. What is the derivative of f(x) = e^x?
a) f'(x) = e^x
b) f'(x) = 1/e^x
c) f'(x) = ln(x)
Answer: a) f'(x) = e^x
5. What is the derivative of f(x) = x^3 + 2x^2 – 5x + 1?
a) f'(x) = 3x^2 + 4x – 5
b) f'(x) = 3x^2 + 4x + 1
c) f'(x) = 4x^2 – 5x + 1
Answer: a) f'(x) = 3x^2 + 4x – 5
6. What is the derivative of f(x) = 1/x?
a) f'(x) = -1/x^2
b) f'(x) = 1/x^2
c) f'(x) = 0
Answer: a) f'(x) = -1/x^2
7. What is the derivative of f(x) = cos(x)?
a) f'(x) = -sin(x)
b) f'(x) = cos(x)
c) f'(x) = tan(x)
Answer: a) f'(x) = -sin(x)
8. What is the derivative of f(x) = x^2 – 4x + 7?
a) f'(x) = 2x – 4
b) f'(x) = 2x – 4x + 7
c) f'(x) = x^2 – 4
Answer: a) f'(x) = 2x – 4
9. What is the derivative of f(x) = ln(x^2 + 1)?
a) f'(x) = 2x / (x^2 + 1)
b) f'(x) = 1 / (x^2 + 1)
c) f'(x) = x / (x^2 + 1)
Answer: a) f'(x) = 2x / (x^2 + 1)
10. What is the derivative of f(x) = sqrt(x)?
a) f'(x) = 1 / (2sqrt(x))
b) f'(x) = 2sqrt(x)
c) f'(x) = 1 / sqrt(x)
Answer: a) f'(x) = 1 / (2sqrt(x))
11. What is the derivative of f(x) = 1/x^3?
a) f'(x) = -3/x^4
b) f'(x) = 3/x^4
c) f'(x) = 0
Answer: a) f'(x) = -3/x^4
12. What is the derivative of f(x) = 5x + sin(x)?
a) f'(x) = 5 + cos(x)
b) f'(x) = 5 – sin(x)
c) f'(x) = 5 + sin(x)
Answer: a) f'(x) = 5 + cos(x)
13. What is the derivative of f(x) = e^(2x+1)?
a) f'(x) = 2e^(2x+1)
b) f'(x) = e^(2x+1)
c) f'(x) = 2e^x
Answer: a) f'(x) = 2e^(2x+1)
14. What is the derivative of f(x) = ln(3x – 2)?
a) f'(x) = 3/(3x – 2)
b) f'(x) = 1/(3x – 2)
c) f'(x) = 0
Answer: b) f'(x) = 1/(3x – 2)
15. What is the derivative of f(x) = tan(x)?
a) f'(x) = sec^2(x)
b) f'(x) = cos(x)
c) f'(x) = sin(x)
Answer: a) f'(x) = sec^2(x)
16. What is the derivative of f(x) = 2cos(x) + 3sin(x)?
a) f'(x) = -2sin(x) + 3cos(x)
b) f'(x) = 2sin(x) + 3cos(x)
c) f'(x) = -2cos(x) + 3sin(x)
Answer: a) f'(x) = -2sin(x) + 3cos(x)
17. What is the derivative of f(x) = 1 / (x^2 + 1)?
a) f'(x) = -2x / (x^2 + 1)^2
b) f'(x) = 2x / (x^2 + 1)^2
c) f'(x) = -1 / (x^2 + 1)^2
Answer: a) f'(x) = -2x / (x^2 + 1)^2
18. What is the derivative of f(x) = 2^x?
a) f'(x) = 2^(x+1)
b) f'(x) = 2^(x-1)
c) f'(x) = ln(2)*2^x
Answer: c) f'(x) = ln(2)*2^x
19. What is the derivative of f(x) = x^4 – 3x^2 + 2?
a) f'(x) = 4x^3 – 6x
b) f'(x) = 4x^3 – 6x^2
c) f'(x) = 4x^4 – 6x^2
Answer: a) f'(x) = 4x^3 – 6x
20. What is the derivative of f(x) = sin(2x)?
a) f'(x) = 2cos(x)
b) f'(x) = cos(2x)
c) f'(x) = 2cos(2x)
Answer: c) f'(x) = 2cos(2x)
21. What is the derivative of f(x) = x^2sin(x)?
a) f'(x) = x^2cos(x)
b) f'(x) = 2xsin(x) + x^2cos(x)
c) f'(x) = 2xsin(x) – x^2cos(x)
Answer: b) f'(x) = 2xsin(x) + x^2cos(x)
22. What is the derivative of f(x) = ln(x^2 + 1)?
a) f'(x) = 2x / (x^2 + 1)
b) f'(x) = 2x / (x^2 + 1)^2
c) f'(x) = 1 / (x^2 + 1)
Answer: a) f'(x) = 2x / (x^2 + 1)
23. What is the derivative of f(x) = (x+1)^2 / (x-2)?
a) f'(x) = 3(x+1)^2 / (x-2)^2
b) f'(x) = (x-2)^2 / (x+1)^2
c) f'(x) = (2x+3) / (x-2)^2
Answer: c) f'(x) = (2x+3) / (x-2)^2
24. What is the derivative of f(x) = e^(sin(x))?
a) f'(x) = cos(x)e^(sin(x))
b) f'(x) = cos(x)
c) f'(x) = e^(sin(x))
Answer: a) f'(x) = cos(x)e^(sin(x))
25. What is the derivative of f(x) = 4x^2 – 2x + 1?
a) f'(x) = 8x – 2
b) f'(x) = 8x – 2x + 1
c) f'(x) = 4x^3 – x^2 + x
Answer: a) f'(x) = 8x – 2
26. What is the derivative of f(x) = ln(cos(x))?
a) f'(x) = -tan(x)
b) f'(x) = -sin(x) / cos(x)
c) f'(x) = -1 / cos(x)
Answer: a) f'(x) = -tan(x)
27. What is the derivative of f(x) = (x^2 – 1)/(x^2 + 1)?
a) f'(x) = 2x / (x^2 + 1)^2
b) f'(x) = -2x / (x^2 + 1)^2
c) f'(x) = 2 / (x^2 + 1)^2
Answer: b) f'(x) = -2x / (x^2 + 1)^2
