Padhai STEM Practice Questions →
NCERT Solutions › Mathematics › Chapter 5

Chapter 5: Continuity & Differentiability

NCERT Solutions for CBSE Class 10 Mathematics — 43 solved questions with detailed explanations.

43
Questions
0
Topics

Solved Questions

Q1. The function f(x) = |x| is:

Difficulty: Easy-Medium · Topic: Continuity

Solution

|x| is continuous for all x. At x=0, left derivative = -1, right derivative = +1. Not differentiable at 0.

Q2. d/dx[e^(sin x)] equals:

Difficulty: Easy-Medium · Topic: Chain Rule

Solution

Chain rule: d/dx[e^(sinx)] = e^(sinx) × cos(x).

Q3. If f is differentiable at a point, then it is:

Difficulty: Easy-Medium · Topic: Continuity & Differentiability

Solution

continuous at that point.

Q4. d/dx(sin⁻¹x) =:

Difficulty: Easy-Medium · Topic: Continuity & Differentiability

Solution

1/√(1-x²).

Q5. d/dx(tan⁻¹x) =:

Difficulty: Easy-Medium · Topic: Continuity & Differentiability

Solution

1/(1+x²).

Q6. d/dx(cos⁻¹x) =:

Difficulty: Easy-Medium · Topic: Continuity & Differentiability

Solution

-1/√(1-x²).

Q7. The derivative of 3x²+2x+1 is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(3x²+2x+1) = 6x+2.

Q8. The derivative of x³-4x is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(x³-4x) = 3x²-4.

Q9. The derivative of 5x⁴ is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(5x⁴) = 20x³.

Q10. The derivative of sin(2x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(sin(2x)) = 2cos(2x).

Q11. The derivative of e^(3x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(e^(3x)) = 3e^(3x).

Q12. The derivative of ln(2x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(ln(2x)) = 1/x.

Q13. The derivative of x²sin(x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(x²sin(x)) = 2xsin(x)+x²cos(x).

Q14. The derivative of e^x·cos(x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(e^x·cos(x)) = e^x(cos(x)-sin(x)).

Q15. The derivative of (x²+1)³ is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx((x²+1)³) = 6x(x²+1)².

Q16. The derivative of 1/(x²+1) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(1/(x²+1)) = -2x/(x²+1)².

Q17. The derivative of √x is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(√x) = 1/(2√x).

Q18. The derivative of x·e^x is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(x·e^x) = e^x(x+1).

Q19. The derivative of sin²(x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(sin²(x)) = sin(2x).

Q20. The derivative of tan(x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(tan(x)) = sec²(x).

Q21. The derivative of e^(x²) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(e^(x²)) = 2xe^(x²).

Q22. The derivative of ln(sin x) is:

Difficulty: Easy-Medium · Topic: Differentiation

Solution

d/dx(ln(sin x)) = cot x.

Q23. d/dx(3x²+2x+1) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(3x²+2x+1) = 6x+2.

Q24. d/dx(x³-4x) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(x³-4x) = 3x²-4.

Q25. d/dx(5x⁴) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(5x⁴) = 20x³.

Q26. d/dx(sin(2x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(sin(2x)) = 2cos(2x).

Q27. d/dx(e^(3x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(e^(3x)) = 3e^(3x).

Q28. d/dx(ln(2x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(ln(2x)) = 1/x.

Q29. d/dx(x²sin(x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(x²sin(x)) = 2xsin(x)+x²cos(x).

Q30. d/dx(e^x·cos(x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(e^x·cos(x)) = e^x(cos(x)-sin(x)).

Q31. d/dx((x²+1)³) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx((x²+1)³) = 6x(x²+1)².

Q32. d/dx(1/(x²+1)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(1/(x²+1)) = -2x/(x²+1)².

Q33. d/dx(√x) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(√x) = 1/(2√x).

Q34. d/dx(x·e^x) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(x·e^x) = e^x(x+1).

Q35. d/dx(sin²(x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(sin²(x)) = sin(2x).

Q36. d/dx(tan(x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(tan(x)) = sec²(x).

Q37. d/dx(e^(x²)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(e^(x²)) = 2xe^(x²).

Q38. d/dx(ln(sin x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(ln(sin x)) = cot x.

Q39. d/dx(x³e^x) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(x³e^x) = e^x(x³+3x²).

Q40. d/dx(cos²(x)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(cos²(x)) = -sin(2x).

Q41. d/dx(√(1+x²)) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(√(1+x²)) = x/√(1+x²).

Q42. d/dx(1/√x) =

Difficulty: Easy-Medium · Topic: Derivatives

Solution

d/dx(1/√x) = -1/(2x√x).

Q43. If y = x^x, then dy/dx is:

Difficulty: Medium · Topic: Logarithmic Diff

Solution

ln y = x ln x. (1/y)dy/dx = ln x + 1. dy/dx = x^x(1 + ln x).

Other Chapters in Mathematics

Ch 1: Relations & FunctionsCh 2: Inverse Trig FunctionsCh 3: MatricesCh 4: DeterminantsCh 6: Applications of DerivativesCh 7: IntegralsCh 8: Applications of IntegralsCh 9: Differential EquationsCh 10: Vector AlgebraCh 11: Three Dimensional GeometryCh 12: Linear ProgrammingCh 13: Probability

Want to practice these questions interactively?

Get instant feedback, track progress, and improve with adaptive practice.

Start Practicing Free →