Chapter 24 of 42
Syllabus
Application of Derivatives — Syllabus
JEE Mains · Mathematics
Topics covered in Application of Derivatives for JEE Mains Mathematics. Understand the syllabus structure and key areas to focus on.
Interactive on Super Tutor
Studying Application of Derivatives? Get the full chapter — free.
Practice questions, revision notes, formula sheet and AI doubt-solver — built for JEE Mains Mathematics.
Super Tutor
This is just one of 9+ visuals inside Super Tutor's Application of Derivatives chapter
Explore the full setApplication of Derivatives — Syllabus & Topics
Topics covered in Application of Derivatives for JEE Mains Mathematics.
Topics in Application of Derivatives
1
Tangent and Normal Lines
- Slope of tangent at point (x₁, y₁) is dy/dx evaluated at that point
- Slope of normal = -dx/dy = -1/(dy/dx) at the point of tangency
- Equation of tangent: (y - y₁) = m(x - x₁) where m = dy/dx at (x₁, y₁)
2
Angle Between Curves
- Angle between two curves = angle between their tangents at point of intersection
- If curves intersect at (x₁, y₁) with slopes m₁ and m₂, then tan θ = |m₁ - m₂|/(1 + m₁m₂)
- Two curves intersect orthogonally if m₁ × m₂ = -1
3
Length of Tangent, Normal, Subtangent, and Subnormal
- Length of tangent = |y|√(1 + (dx/dy)²)
- Length of normal = |y|√(1 + (dy/dx)²)
- Length of subtangent = |y| |dx/dy|
4
Rate of Change and Related Rates
- Rate of change = dy/dt where y is the changing quantity and t is time
- For related rates: if x and y are related by equation f(x,y) = 0, then differentiate implicitly with respect to time
- Chain rule is essential: dy/dt = (dy/dx) × (dx/dt)
Key Concepts
For a curve y = f(x)The angle θ between two curvesFor curve y = f(x) atDerivatives represent instantaneous rates of changeFor small changes
Frequently Asked Questions
What topics are covered in Application of Derivatives for JEE Mains?
Application of Derivatives is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Tangent and Normal Lines, Angle Between Curves, Length of Tangent, Normal, Subtangent, and Subnormal, Rate of Change and Related Rates.
How important is Application of Derivatives for JEE Mains?
Application of Derivatives is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 68 practice questions available for this chapter.
How to prepare Application of Derivatives for JEE Mains?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.
More resources for Application of Derivatives
For JEE Mains aspirants
Get the full Application of Derivatives chapter — for free.
Practice questions, revision notes, formula sheet and AI doubt-solver for JEE Mains Mathematics.