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  • CALCULUS CONTENT
  • Calculus Home
      • A.1 First Calculations
      • A.2 Generalizing to Other Rates of Change
      • A.3 Introducing Linear Approximations
      • A.4 Practice Problems: Linear Approximations
      • A.5 Differentials; Steps Toward Determining 𝑑𝑓𝑑𝑥 at 𝑥 =𝑎
      • A.6 Estimating 𝑑𝑓𝑑𝑥 at 𝑥 =𝑎 Graphically
      • B.1 Average Velocity for a Trip
      • B.2 Average Velocity Over Any Interval
      • B.3 Generalizing Average Rate of Change
      • B.4 Lab 1 Introduction: Approximate & Bound Error for 𝑑𝑓𝑑𝑥
      • B.5 Lab 1 Activity: Approximate & Bound Error of 𝑑𝑓𝑑𝑥
      • A.1 Introduction to Limits
      • A.2 Tolerance & Pancake Story
      • A.3 Epsilon-Delta Formal Definition
      • A.4 Lab: Find Limit Using Approximations
      • A.5 Limits That Exist & Do Not
      • A.6 One-Sided Limits
      • A.7 Vertical Asymptotes
      • B.1 Limit Laws
      • B.2 Substitution to Find a Limit
      • B.3 Factor to Find a Limit
      • B.4 Use Conjugates to Find a Limit
      • B.5 Use Algebra to Find a Limit
      • B.6 The Squeeze Theorem
      • B.7 Special Trig Limits
      • C.1 Introduction to Limits at Infinity
      • C.2 The Epsilon Strip
      • C.3 Some Limits at Infinity That Exist; Some That Do Not
      • C.4 Some Limits at Negative Infinity That Exist; Some That Do Not
      • C.5 Limits of Polynomials
      • C.6 Limits of Rational Functions
      • C.7 Limits of Exponential and Logarithmic Functions
      • C.8 Limits at Infinity with Square Roots
      • D.1 Continuity at a Point and Over an Interval
      • D.2 Discontinuity Types: Removable Discontinuities
      • D.3 Continuous functions; Continuity theorems
      • D.4 The Intermediate Value Theorem
      • A.1 Derivatives of Constant, Linear, and Power Functions
      • A.2 Derivative of Exponential Functions
      • A.3 Derivatives of sin⁡𝑥 and cos⁡𝑥
      • B.1 The Product Rule
      • B.2 The Quotient Rule
      • C.1 Conceptual Understanding of the Chain Rule
      • C.2 The Chain Rule
      • C.3 Basic Practice with the Chain Rule
      • C.4 Deeper Work with the Chain Rule
      • C.5 Chain Rule - Used to Find Yet More Derivatives
      • D.1 Explicitly and Implicitly Defined Functions
      • D.2 Implicit Differentiation
      • E.2 Derivative of Inverse Functions
      • F.1 Derivative of ln⁡(𝑥)
      • Derivative Rules: Practice Problems & Solutions
      • Chain Rule: Practice Problems & Solutions
    • • Tangent & Normal Lines
    • • Maxima & Minima
    • • Curve Sketching
    • • Mean Value Theorem
    • • Approximations
    • • L'Hôpital's Rule
    • • Related Rates
    • • Optimization
    • • Definite Integration
    • • Indefinite Integration
    • • u-substitution
    • • List of all blog posts
    • • 4 Steps to Solve Related Rates Problems in Calculus - Part 1
    • • 4 Steps to Solve Related Rates Problems in Calculus - Part 2
    • • How to Solve Optimization Problems in Calculus
    • • 0 Divided by 0: Solve Limit Problems in Calculus, Part 1
    • • 0 Divided by 0: Solve Limit Problems in Calculus, Part 2
    • • Helping You with Calculus: Introducing Matheno
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V. Derivative Applications

Time to put those derivatives to use! Let's work through typical application problems step-by-step.

Derivative Applications chapter image

Topics in this Chapter

  • Tangent & Normal Lines
  • Maxima & Minima
  • Curve Sketching
  • Mean Value Theorem
  • Approximations
  • L'Hôpital's Rule
  • Related Rates
  • Optimization
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