Insights By Scott Ernst

Project Autodidact

Project Details: https://insightsbyse.com/projectautodidact/

Scott Ernst Bio: https://insightsbyse.com/aboutscotternst/

Project Contact: InsightsBySE@protonmail.com

Progress Report Scope (S01-M03-D03-AllParts)

Stage 1 of 4: Review of Mathematics, Probability, and Statistics

Module 3 of 3: Linear Algebra, Calculus, and Applications

Day 3 of 5: Derivatives and Applications

Parts 1 through 8: See below (NOTE: Only 8 parts for these topics)

Summary Of Goals Achieved

1. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of a derivative in calculus, including the distinction among a first, second, and third derivative
2. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of a partial derivative in calculus
3. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of non-differentiable functions in calculus
4. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of infinitely differentiable functions in calculus
5. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of higher-order derivatives in calculus
6. Reviewed similarities and differences between the difference quotient and the derivative in calculus
7. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for calculating derivatives in calculus, including partial and higher-order derivatives
8. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the constant rule for derivatives in calculus
9. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the constant multiple rule for derivatives in calculus
10. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the sum and difference rule for derivatives in calculus
11. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the power rule for derivatives in calculus
12. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the product rule for derivatives in calculus
13. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the quotient rule for derivatives in calculus
14. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of the chain rule for derivatives in calculus
15. Reviewed definition, concepts, notation, terminology, components, and properties of composite functions in calculus
16. Reviewed definition, concepts, notation, terminology, components, and properties of nested derivatives in calculus
17. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for creating and evaluating composite functions
18. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for creating and evaluating nested derivatives
19. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for solving the problem of vanishing and exploding gradients
20. Reviewed definition, concepts, notation, terminology, components, and properties of derivative formulas for exponents, roots, general logarithms, and natural logarithms
21. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for finding the derivatives for exponents, roots, general logarithms, and natural logarithms
22. Reviewed similarities and differences between critical points and inflection points in calculus
23. Reviewed definition, concepts, notation, terminology, components, properties, and procedures for using the first derivative in calculus to analyze function behavior, including critical points
24. Reviewed definition, concepts, notation, terminology, components, properties, and procedures for using the second derivative in calculus to analyze function behavior, including stationary and non-stationary inflection points, and determine concavity
25. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for finding and analyzing critical points and inflection points in calculus
26. Reviewed similarities and differences among critical points, inflection points, and extrema in calculus
27. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for applying derivatives to optimization problems, including optimization constraints
28. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for using derivatives for rate-of-change analysis in datasets
29. Reviewed definition, concepts, notation, terminology, components, and properties of implicit differentiation in calculus
30. Reviewed definition, concepts, notation, terminology, components, and properties of dependent variables in calculus
31. Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for implicit differentiation in calculus

Part 1 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of a derivative in calculus, including the distinction among a first, second, and third derivative

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of a partial derivative in calculus

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of non-differentiable functions in calculus

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of infinitely differentiable functions in calculus

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of higher-order derivatives in calculus

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review similarities and differences between the difference quotient and the derivative in calculus

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for calculating derivatives in calculus, including partial and higher-order derivatives

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal 7 Result: Completed

Part 2 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the constant rule for derivatives in calculus

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the constant multiple rule for derivatives in calculus

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the sum and difference rule for derivatives in calculus

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the power rule for derivatives in calculus

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the product rule for derivatives in calculus

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the quotient rule for derivatives in calculus

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of the chain rule for derivatives in calculus

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal 7 Result: Completed

Part 3 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of composite functions in calculus

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, and properties of nested derivatives in calculus

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for creating and evaluating composite functions

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for creating and evaluating nested derivatives

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for solving the problem of vanishing and exploding gradients

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 4 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of derivative formulas for exponents, roots, general logarithms, and natural logarithms

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for finding the derivatives for exponents, roots, general logarithms, and natural logarithms

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 5 of 8

Goal 1 Statement: Review similarities and differences between critical points and inflection points in calculus

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and procedures for using the first derivative in calculus to analyze function behavior, including critical points

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and procedures for using the second derivative in calculus to analyze function behavior, including stationary and non-stationary inflection points, and determine concavity

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for finding and analyzing critical points and inflection points in calculus

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Part 6 of 8

Goal 1 Statement: Review similarities and differences among critical points, inflection points, and extrema in calculus

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for applying derivatives to optimization problems, including optimization constraints

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 7 of 8

Goal 1 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for using derivatives for rate-of-change analysis in datasets

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Part 8 of 8

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of implicit differentiation in calculus

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, and properties of dependent variables in calculus

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for implicit differentiation in calculus

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed