Continuity and Differentiability for JEE

• Continuous at a: LHL = RHL = f(a)
• Differentiable implies continuous, not the reverse
• |x| is continuous but not differentiable at 0
• Greatest integer function is discontinuous at integers

• Chain rule: d/dx f(g(x)) = f′(g(x))g′(x)
• Parametric: dy/dx = (dy/dt)/(dx/dt)
• Logarithmic differentiation for xˣ type functions
• d/dx (sin⁻¹x) = 1/√(1 − x²)

Printable Continuity and Differentiability formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

• Checking only one side
• Assuming continuity means differentiability
• Wrong derivative of inverse trig functions

Appears frequently. Questions on |x|, [x] and piecewise functions are very common.

Prerequisites: Limits.

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Question. Let f(x) = |x³ - x| for x ∈ [-1, 2]. Find the number of points in the interval where f(x) is not differentiable.

This example was solved twice independently and both solutions agree.

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

• LIMIT, CONTINUITY & DIFFERENTIABILITY in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:35:05
  Jump to a subtopic (25)

  • 00:00 Introduction
  • 04:57 Topics to be covered
  • 07:19 Limit at a point x=a
  • 36:24 Some standard limits
  • 1:23:21 Exponential limits
  • 1:34:54 Logarithmic limits
  • 1:46:48 Algebraic limits
  • 1:52:56 Various methods to solve limits
  • 2:10:52 Solving limits using L’Hospital rule
  • 2:11:23 Indeterminate forms
  • 2:46:15 Solving limits of the form 1 power infinity
  • 3:00:50 Solving limits using series expansion
  • 3:23:26 Solving limits using sandwich theorem
  • 3:32:45 Continuity at a point x=a
  • 3:53:59 Continuity in an interval
  • 4:19:24 Properties of continuous function
  • 4:32:45 Break
  • 5:02:27 Differentiability at a point x=a and In an interval
  • 5:19:38 Geometrical interpretation of differentiability
  • 5:20:48 Continuity Vs Differentiatiability
  • 5:44:52 Continuity over an interval
  • 5:55:14 Properties of differentiable function
  • 6:08:38 Functional identities
  • 6:33:00 Homework
  • 6:33:43 Thank You Bacchon
• Continuity and Differentiability Class 12 | JEE Main & Advanced — JEE Nexus by Unacademy, 3:57:41
  Jump to a subtopic (10)

  • 0:00 Introduction and nature of chapter
  • 2:33 Index and critical topics
  • 4:41 Continuity at a point
  • 1:29:48 Continuity of Composite functions
  • 1:58:57 Continuity in an interval
  • 2:07:48 Types of Discontinuity
  • 2:15:11 Intermediate value theorem
  • 2:21:08 LHD and RHD at x = a
  • 2:33:32 Differentiability at a point
  • 3:49:18 Differentiability in an interval

• 9 JEE Main 2026 PYQs on Continuity and Differentiability, with solutions.
• Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
• Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
• Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
• See it move: interactive simulation.