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Chapter 3 of 10
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.

45 questions20 flashcards5 concepts

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)

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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

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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.

Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

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