Skip to main content
Super TutorResources
Chapter 3 of 10
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Revision Notes

Differentiation and its Applications

CBSE · Class 12 · Applied Mathematics

Quick revision notes for Differentiation and its Applications — CBSE Class 12 Applied Mathematics. Key concepts, formulas, and definitions for last-minute revision.

49 questions20 flashcards5 concepts

Interactive on Super Tutor

Studying Differentiation and its Applications? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

Key Topics to Revise

1

Differentiation of Implicit Functions

  • Implicit functions are equations where y cannot be expressed explicitly as y = f(x)
  • We differentiate both sides of the equation with respect to x, treating y as a function of x
  • Use chain rule: d/dx(y²) = 2y·dy/dx
2

Differentiation of Parametric Functions

  • Parametric equations express both x and y in terms of a parameter t: x = f(t), y = g(t)
  • dy/dx = (dy/dt)/(dx/dt), provided dx/dt ≠ 0
  • Common parametric forms include circles, parabolas, and cycloids
3

Logarithmic Differentiation

  • Used for functions of the form [f(x)]^g(x) where both base and exponent contain x
  • Take natural logarithm of both sides before differentiating
  • Apply product rule to log y = g(x)·log f(x)
4

Second and Higher Order Derivatives

  • Second derivative: d²y/dx² = d/dx(dy/dx)
  • Third derivative: d³y/dx³ = d/dx(d²y/dx²)
  • Higher order derivatives: d^n y/dx^n = f^(n)(x)

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A technique used when y cannotWhen both x and yUsed for functions of the formSecond derivative d²y/dx² is the derivativeCost function C(x) = Variable cost

Frequently Asked Questions

What are the important topics in Differentiation and its Applications for CBSE Class 12 Applied Mathematics?
Differentiation and its Applications covers several key topics that are frequently asked in CBSE Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Differentiation and its Applications — CBSE Class 12 Applied Mathematics?
Understand the core concepts first, then work through the 49 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Differentiation and its Applications

All 10 chapters — CBSE Class 12 Applied Mathematics Revision Notes

For serious students

Get the full Differentiation and its Applications chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for CBSE Class 12 Applied Mathematics.

Try Super Tutor Free
Try the full chapter — Free