Chapter 24 of 42
Revision Notes
Application of Derivatives — Revision Notes
JEE Advanced · Mathematics
Quick revision notes for Application of Derivatives — key concepts, formulas, and definitions for JEE Advanced Mathematics preparation.
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Key concepts, formulas, and definitions from Application of Derivatives for JEE Advanced Mathematics preparation.
Key Topics to Revise
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)
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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 Advanced?
Application of Derivatives is an important chapter in JEE Advanced 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 Advanced?
Application of Derivatives is a frequently tested chapter in JEE Advanced 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 Advanced?
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.
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