Derivative of a constant MCQs With Answer

Mastering the derivative of a constant is essential for B. Pharm students studying calculus applications in pharmacokinetics, drug formulation, and quantitative analysis. This concise, Student-friendly post explains the constant rule, why the derivative of a constant equals zero, implications for higher-order and partial derivatives, and limit-based proofs that underpin the concept. The resource uses targeted keywords like “Derivative of a constant MCQs With Answer”, “constant derivative”, “differentiation rules”, and “B. Pharm” to help your exam preparation and online search. Practical examples link theory to concentration–time curves and lab calculations to deepen understanding. This set titled “Derivative of a constant MCQs With Answer” is tailored for B. Pharm exam prep and class assessments. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the derivative of a constant c with respect to x?

• 0
• c
• 1
• Undefined

Correct Answer: 0

Q2. Evaluate d/dx(7).

• 7
• 0
• 1
• Does not exist

Correct Answer: 0

Q3. What is d/dx(π)?

• π
• 1
• 0
• Undefined

Correct Answer: 0

Q4. If f(x) = -3, what is f'(x)?

• -3
• 0
• 1
• Cannot determine

Correct Answer: 0

Q5. What is the derivative of the zero function f(x)=0?

• 0
• 1
• Undefined
• Depends on x

Correct Answer: 0

Q6. What is the second derivative d^2/dx^2 (5)?

• 5
• 0
• Undefined
• 1

Correct Answer: 0

Q7. The slope of a constant function y = C is:

• Equal to C
• Zero
• One
• Undefined

Correct Answer: Zero

Q8. If plasma concentration y(t) remains constant over time, dy/dt equals:

• A positive constant
• Negative constant
• Zero
• Depends on dose

Correct Answer: Zero

Q9. Evaluate d/dx(c*x) where c is a constant.

• c
• x
• 0
• 1

Correct Answer: c

Q10. According to the constant multiple rule, d/dx[c·f(x)] equals:

• c + f'(x)
• c · f'(x)
• f'(x)
• 0

Correct Answer: c · f'(x)

Q11. For f(x) = 5x + 3, what is the derivative of the constant term 3?

• 3
• 1
• 0
• Depends on x

Correct Answer: 0

Q12. The derivative of a constant with respect to y is:

• Depends on x
• Zero
• One
• Undefined

Correct Answer: Zero

Q13. What is the partial derivative ∂/∂x (6) for a multivariable function?

• 6
• 0
• 1
• Cannot be computed

Correct Answer: 0

Q14. Given e^0 = 1, what is d/dx(1)?

• 1
• e^x
• 0
• Undefined

Correct Answer: 0

Q15. If f(x) = ln(e), what is f'(x)?

• 1/x
• 0
• 1
• ln(e)

Correct Answer: 0

Q16. d/dx(c^2) where c is a constant equals:

• 2c
• c
• 0
• Depends on x

Correct Answer: 0

Q17. In pharmacokinetics, if concentration is constant over time, the net rate of change is:

• Positive
• Negative
• Zero
• Equal to concentration

Correct Answer: Zero

Q18. By the limit definition, d/dx(c) = lim(h→0) [c – c]/h equals:

• c/h
• 1
• 0
• Undefined

Correct Answer: 0

Q19. Which differentiation rule directly states the derivative of a constant is zero?

• Product rule
• Quotient rule
• Constant rule
• Chain rule

Correct Answer: Constant rule

Q20. d/dx (5 + x^2) equals:

• 5 + 2x
• 2x
• 0
• 2

Correct Answer: 2x

Q21. If f(x)=a·e^x + b where b is constant, f'(x) equals:

• a·e^x + b
• a·e^x
• b
• 0

Correct Answer: a·e^x

Q22. If f'(x) = 0 for all x in an interval, then f(x) must be:

• A linear function
• An exponential function
• A constant function
• Undefined

Correct Answer: A constant function

Q23. True or False: The derivative of a constant is zero only sometimes.

• True
• False
• Depends on the variable
• Only if constant is zero

Correct Answer: False

Q24. What is d/dx(N_A) where N_A is Avogadro’s number (a constant)?

• N_A
• 1
• 0
• Depends on mole

Correct Answer: 0

Q25. The time derivative d/dt of a fixed parameter constant in a rate law equals:

• The parameter itself
• 1
• 0
• Depends on t

Correct Answer: 0

Q26. What is d/dx(10^0)?

• 10
• 0
• 1
• Undefined

Correct Answer: 0

Q27. The derivative of a constant added to a function f(x) affects the derivative how?

• Shifts it vertically
• Changes amplitude
• Does not change it
• Makes it zero

Correct Answer: Does not change it

Q28. d/dx [k·sin x] where k is constant equals:

• k·cos x
• sin x
• k·sin x
• 0

Correct Answer: k·cos x

Q29. Adding a constant to any differentiable function will:

• Alter its derivative everywhere
• Leave its derivative unchanged
• Multiply the derivative by the constant
• Make the derivative undefined

Correct Answer: Leave its derivative unchanged

Q30. If f'(x)=0 on an interval, general solution for f(x) is:

• f(x) = ax + b
• f(x) = constant
• f(x) = e^x
• f(x) = 0 only

Correct Answer: f(x) = constant

Q31. Numerically approximating derivative of a constant function yields:

• Zero (within rounding errors)
• A large number
• Undefined
• Oscillatory values

Correct Answer: Zero (within rounding errors)

Q32. Evaluate d/dx(c^x) where c is a constant base (c > 0, c ≠ 1).

• 0
• c^x · ln c
• x · c^{x-1}
• ln x

Correct Answer: c^x · ln c

Q33. d/dx(5·ln x + 3) equals:

• 5·ln x + 3
• 5/x
• 3
• 0

Correct Answer: 5/x

Q34. In drug concentration context, dC/dt = 0 implies:

• Concentration is increasing
• Concentration is constant
• Concentration is decreasing
• Concentration is undefined

Correct Answer: Concentration is constant

Q35. Adding a constant to f(x) produces which graph transformation?

• Horizontal shift
• Vertical shift
• Stretch
• Reflection

Correct Answer: Vertical shift

Q36. d/dx (C·0) where C is constant equals:

• C
• 0
• Depends on x
• Undefined

Correct Answer: 0

Q37. If f'(x0) = 0 at a single point x0, then:

• f has a local extremum at x0 always
• f is constant globally
• f may have extremum, inflection, or neither at x0
• Derivative undefined elsewhere

Correct Answer: f may have extremum, inflection, or neither at x0

Q38. Which is the derivative of the constant function f(x)=M?

• M
• 1
• 0
• Depends on x

Correct Answer: 0

Q39. Higher-order derivatives of a constant are:

• Increasing
• Alternating
• All zero
• Undefined

Correct Answer: All zero

Q40. Simplify d/dx (π·x^0).

• π
• 0
• x
• 1

Correct Answer: 0

Q41. Which limit shows the derivative of a constant c is zero?

• lim(h→0) (c+h – c)/h
• lim(h→0) (c – c)/h
• lim(h→0) (c·h)/h
• lim(h→0) c/h

Correct Answer: lim(h→0) (c – c)/h

Q42. If a parameter C does not depend on time, dC/dt is:

• Nonzero constant
• Variable
• Zero
• Equal to C

Correct Answer: Zero

Q43. The partial derivative ∂/∂y of a constant number is:

• 1
• 0
• Same as the number
• Undefined

Correct Answer: 0

Q44. If f'(x) = 0 for all x, what constant appears in the antiderivative F(x)?

• No constant
• Arbitrary constant C
• Zero only
• Only positive constants

Correct Answer: Arbitrary constant C

Q45. d/dx(7 + sin x) equals:

• 7 + cos x
• cos x
• sin x
• 0

Correct Answer: cos x

Q46. For p(x)=x^3+4x+2, p'(x) equals:

• 3x^2 + 4
• x^2 + 4
• 2
• 3x^2 + 4x

Correct Answer: 3x^2 + 4

Q47. Which of the following is NOT a constant?

• 5
• π
• x
• e

Correct Answer: x

Q48. If y = C/x where C is constant, is y a constant function?

• Yes, always
• No, it varies with x
• Only if x=1
• Only if C=0

Correct Answer: No, it varies with x

Q49. The total derivative d/dt of a constant C equals:

• C
• 1
• 0
• Depends on variable substitution

Correct Answer: 0

Q50. If dy/dx = 0 on an interval, the general solution for y is:

• y = ax + b
• y = constant
• y = 0 only
• y = x^2

Correct Answer: y = constant

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