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Differentiation and its Applications — Syllabus

CBSE · Class 12 · Applied Mathematics

What Differentiation and its Applications covers in CBSE Class 12 Applied Mathematics: 4 topics, for the 2026-27 session.

48 questions20 flashcards7 formulas & key relations5 concepts

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4 Topics · CBSE Class 12 Applied Mathematics · 2026-27

Topics in Differentiation and its Applications

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)

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?
Key topics in Differentiation and its Applications include Differentiation of Implicit Functions, Differentiation of Parametric Functions, Logarithmic Differentiation, Second and Higher Order Derivatives. Study these first, then practise questions on each for the CBSE Class 12 board exam.
How should I revise Differentiation and its Applications for the CBSE Class 12 board exam?
Learn the core ideas first, then work through the 48 practice questions on Differentiation and its Applications. Revise 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.

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All CBSE Class 12 Applied Mathematics Syllabus

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