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Application of Derivatives is one of the most scoring and conceptually important chapters in JEE Mathematics. This chapter applies the concepts of differentiation to real and graphical problems, making it a bridge between theory and application. Questions from this chapter appear regularly in JEE Main and JEE Advanced, often testing conceptual clarity rather than lengthy calculations.
A strong understanding of this topic helps students analyze functions, interpret graphs, and solve optimization problems efficiently.
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♦ Set Theory and Relations ⇒ Download Here
♦ Function ⇒ Download Here
♦ Differentiation ⇒ Download Here
♦ Application of Derivatives ⇒ Download Here
♦ Indefinite Integral ⇒ Download Here
♦ Definite Integral ⇒ Download Here
♦ Area Under Curve ⇒ Download Here
♦ Differential Equations ⇒ Download Here
♦ Vector Algebra ⇒ Download Here
♦ 3D Dimensional ⇒ Download Here
♦ Determinants ⇒ Download Here
♦ Binary ⇒ Download Here
♦ Logarithm ⇒ Download Here
♦ Complex Number ⇒ Download Here
♦ Progression ⇒ Download Here
♦ Quadratic Equation ⇒ Download Here
♦ Permutations and Combinations ⇒ Download Here
♦ Binomial Theorem ⇒ Download Here
♦ Exponential ⇒ Download Here
♦ Rectangular Cartesian Co-ordinates ⇒ Download Here
♦ Straight Lines ⇒ Download Here
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♦ Circle System ⇒ Download Here
♦ Conic Sections ⇒ Download Here
♦ Trigonomerical Ratio ⇒ Download Here
♦ Trigonomerical Equation ⇒ Download Here
♦ Trigonomerical Properties ⇒ Download Here
♦ Height & Distances ⇒ Download Here
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♦ Statics ⇒ Download Here
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♦ Maths Formula PDF for Entrance Exam ⇒ Download Here
Derivatives measure the rate of change of a function. The application of derivatives uses this idea to study the behavior of functions, such as whether a function is increasing or decreasing, where it reaches maximum or minimum values, and how curves behave geometrically.
This chapter builds directly on differentiation and prepares students for advanced calculus topics.
Rate of change is one of the most basic applications of derivatives. It describes how one quantity changes with respect to another.
In JEE Maths, rate of change problems may involve:
Change of distance with time
Change of area with dimensions
Change of volume or physical quantities
These questions test the ability to apply derivatives to real-life situations.
A function’s behavior is determined using its first derivative:
If f′(x) > 0, the function is increasing
If f′(x) < 0, the function is decreasing
JEE frequently asks students to find intervals of increase and decrease, often combined with graph-based or inequality-based questions.
A function is said to be monotonic if it is either increasing or decreasing over an interval.
Understanding monotonicity helps in:
Graph analysis
Solving inequality-based problems
Comparing function values
This concept is widely used in JEE Advanced problems.
Maxima and minima represent the highest and lowest values of a function in a given interval.
Key ideas include:
First derivative test
Critical points where f′(x) = 0 or undefined
JEE problems often require identifying turning points and analyzing the nature of extrema.
The second derivative provides information about the nature of extrema:
f′′(x) > 0 → Local minimum
f′′(x) < 0 → Local maximum
This method is commonly used in JEE to save time and improve accuracy.
In addition to local extrema, JEE Maths also tests absolute maximum and minimum values of functions over closed intervals.
These problems require:
Finding critical points
Evaluating function values at endpoints
Comparing results logically
Such questions are common in JEE Main.
One of the most popular applications of derivatives in JEE is finding equations of tangents and normals to curves.
Important concepts include:
Slope of tangent using derivative
Equation of tangent at a point
Equation of normal perpendicular to tangent
These questions may involve algebraic curves, parametric curves, or implicit functions.
Derivatives are also used to find the angle of intersection between two curves.
JEE tests:
Angle between tangents
Orthogonal intersection conditions
Trigonometric interpretation of slopes
This topic is especially important for JEE Advanced.
Derivatives can be used to find approximate values and errors in measurements.
Applications include:
Estimating small changes
Error propagation
Linear approximation
Though less frequent, these problems test conceptual understanding.
Geometrically, derivatives represent:
Slope of tangent
Nature of curve at a point
Shape and behavior of graphs
Many JEE questions rely on interpreting graphs rather than direct calculations.
Optimization problems involve finding maximum or minimum values under given conditions.
Examples include:
Maximizing area or volume
Minimizing cost or distance
Real-life word problems
These questions test logical thinking and step-by-step problem-solving ability.
Some frequent errors include:
Incorrect differentiation
Ignoring domain restrictions
Wrong identification of critical points
Confusion between local and absolute extrema
Avoiding these mistakes can significantly improve JEE performance.
This chapter is important because it:
Directly appears in every JEE paper
Tests real-world application skills
Strengthens graph interpretation
Supports advanced calculus topics
Mastery of this chapter ensures better confidence in calculus.
Practice a variety of problems daily
Focus on graphical understanding
Revise differentiation rules
Solve previous year JEE questions
Using well-structured content from StudentBro helps students build strong fundamentals and exam readiness.
Application of Derivatives is a high-scoring and concept-driven chapter in JEE Mathematics. With clear understanding, consistent practice, and proper analysis, students can easily master this topic. StudentBro provides exam-focused explanations and problem-solving strategies to help JEE aspirants excel confidently.
