# CALCULAS MCQs

# 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**