The Quotient Rule

Limits

1. Introduction to Limits
2. What is a limit?
3. What is Infinity?
4. Limits, and Infinity
5. Are Limits Real?
6. Limits, and the Cartesian Plane
7. Trickster limits
8. Limits From the Right, and the Left
9. The Difference Between Horizontal and Vertical Asymptotes
10. Limit Notation

Differentiation Basics

1. Introduction to Calculus
2. Mathematically Describing a Changing World
3. How Can We Figure Out the Gradient of a Curve
4. The Gradient Function
5. The Symbol for the Gradient Function
6. Finding the Gradient Function – Part 1
7. Finding the Gradient Function – Part 2
8. Finding the Gradient Function – Part 3
9. Finding the Gradient Function – Part 4
10. Finding the Gradient Function – Part 5
11. Finding the Gradient Function – Part 6
12. Matching a Curve and its Gradient Function
13. Increasing, or Decreasing – Part 1
14. Increasing, or Decreasing – Part 2
15. Increasing, or Decreasing – Part 3
16. Proving Differentiation Finds the Gradient Function – Part 1
17. Proving Differentiation Finds the Gradient Function – Part 2
18. Proving Differentiation Finds the Gradient Function – Part 3
19. Proving Differentiation Finds the Gradient Function – Part 4
20. Proving Differentiation Finds the Gradient Function – Part 5
21. dy/dx Notation – Part 1
22. dy/dx Notation – Part 2
23. dy/dx Notation – Part 3
24. dy/dx Notation – Part 4
25. Equation of a Tangent to a Curve
26. Equation of a Normal to a Curve
27. Locating Stationary Points
28. Identifying Stationary Points
29. Sketching the Gradient Function – Part 1
30. Sketching the Gradient Function – Part 2
31. Sketching the Gradient Function – Part 3
32. S
33. ketching the Gradient Function – Part 4
34. Higher-Order Derivatives
35. Rate of change
36. Identifying Stationary Points Using Second-Order Derivatives

Differentiating Non-Algebraic Functions

1. Introduction to Differentiating Non-Algebraic Functions
2. When the Old Method Breaks Down
3. Differentiating ln(x)
4. Differentiating Other Log Functions
5. The Change of Base Formula
6. Differentiating sin(kx)
7. Differentiating cos(kx)
8. Differentiating tan(kx)
9. Differentiating cot(kx)
10. Differentiating sec(kx)
11. Differentiating cosec(kx)
12. Solving Problems with Non-Algebraic Curves
13. Rheya and the Trigadorian Cloud
14. Prove it All Night
15. Holes in Graphs
16. Using Limits to Mend Holes
17. Mending Holes: A Special Case
18. Mending Holes: Another Special Case
19. Proving the Gradient Function of sin(x) Part 1
20. Proving the Gradient Function of sin(x) Part 2
21. Proving the Gradient Function of cos(x) Part 1
22. Proving the Gradient Function of cos(x) Part 2

Differentiating Combined Functions

1. Introduction to Differentiating Combined Functions
2. The Chain Rule
3. The Power of the Chain Rule
4. Making Functions Composite Before Differentiating
5. The Chain Rule in Leibniz’s Notation
6. Finding Your Inner Function
7. Algebraic Inner Functions
8. Trigonometric Inner Functions
9. Exponential Inner Functions
10. Logarithmic Inner Functions
11. The Product Rule
12. The Power of the Product Rule
13. Splitting Functions into Products Before Differentiating
14. The Product Rule in Leibniz’s Notation
15. Finding Your Factors
16. Using the Chain Rule and Product Rule Together
17. The Quotient Rule
18. Splitting Fractions Apart Before Differentiating
19. The Quotient Rule in Leibniz’s Notation
20. Just Use the Numerator and Denominator
21. Using the Chain Rule and Quotient Rule Together
22. Using the Product Rule and Quotient Rule Together
23. Using All Three Rules Together
24. Using All Three Rules Together
25. Proving the Derivatives of Cosec and Sec
26. Proving the Derivatives of Tan and Cot

Differentiating Implicit Equations

1. Introduction to Differentiating Implicit Equations
2. Explicit and Implicit Equations
3. Rearranging Implicit Equations
4. Differentiating Implicit Equations by Rearranging
5. Differential Equations
6. Rearranging Differential Equations
7. Implicit Differentiation Part 1
8. Implicit Differentiation Part 2
9. The Chain Rule Allows us to Differentiate Implicitly
10. Implicit Differentiation and the Product Rule
11. Implicit Differentiation and Fractions
12. Solving Problems with Implicit Differentiation
13. Getting Two Different Gradient Functions

Differentiating Parametric Equations

1. Introduction to Differentiating Parametric Equations
2. Differentiating Parametric Equations
3. Finding the Gradient Function in Parametric Form
4. Finding Stationary Points Using a Parameter
5. Finding Tangents and Normals Using a Parameter

The Second Derivative

1. Introduction to the Second Derivative
2. Convex and Concave Curves
3. The Gradient Value at Convex and Concave Intervals
4. Are Straight Lines Convex or Concave?
5. Using the Second Derivative
6. Intervals in Which Functions are Convex or Concave
7. Revisiting Points of Inflection
8. The Second Derivative at Points of Inflection
9. Using the Second Derivative to find Points of Inflection