NCERT Mathematics, Class 12, textbook pages 104–146 (Part I)

How to help your child with Class 12 Maths Chapter 5, Continuity and Differentiability, at home

Continuity, chain rule and advanced derivatives, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

continuous, notdifferentiable at 0

NCERT Class 12 Maths Chapter 5 Continuity and Differentiability: what it teaches

Your teen checks continuity, differentiates composite, implicit, inverse trig, exponential and logarithmic functions, uses logarithmic differentiation, and finds second derivatives.

Why it matters later. These techniques are needed for applications of derivatives and integration.

See it: this chapter in pictures

d/dx sin(x²)= cos(x²) · 2xchain rule
Outer times inner derivative.
x² + y² = 252x + 2y y′ = 0y′ = −x/y
Differentiate both sides.
y = xˣ → ln y = x ln xy′/y = ln x + 1y′ = xˣ(1 + ln x)
Take logs first.

You need

  • a formula sheet
  • graph paper

Tonight’s 60 minutes

  1. Check continuity of f(x) = |x| at 0 (continuous) and differentiability (not).
  2. Differentiate sin(x²) with the chain rule.
  3. Differentiate x² + y² = 25 implicitly.
  4. Use logarithmic differentiation for xˣ.

Words to use

  • continuous
  • differentiable
  • chain rule
  • implicit
  • logarithmic differentiation
  • second derivative

Watch for

  • Forgetting the inner derivative. Chain rule: outer derivative × inner derivative.
  • Assuming continuous means differentiable. |x| is continuous but not differentiable at 0.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

Youd/dx sin(x²)?

Your childcos(x²) × 2x.

A game for this week: Chain rule relay

  1. Write composite functions on cards.
  2. Each player differentiates one layer.
  3. Pass to the next.
  4. Check the final answer.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Rates in physics.
  • Economics marginal analysis.
  • Engineering curves.
  • Biology growth rates.

Quick check

Ask these at the end of the week. Tap to see the answer.

d/dx sin(x²)?

2x cos(x²).

dy/dx for x² + y² = 25?

−x/y.

d/dx xˣ?

xˣ(1 + ln x).

Ready for the next chapter when your child…

  • Checks continuity and differentiability.
  • Uses chain, implicit and log differentiation.
  • Finds second derivatives.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

Is every continuous function differentiable?

No: |x| at 0 is a classic example.

What is implicit differentiation?

Differentiating both sides when y isn’t isolated.

When use logarithmic differentiation?

For powers like xˣ or long products.