YOU are better than YOU think. Show yourself  how:  

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 Logic chapters 1 to 5  re- appear not in sequence, as is or longer,  in  Volume 1A,  Pattern Based Reason, Bon Appetite.

Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and
writing

Logic mastery makes the hard, easier. Logic mastery  leads to better, stronger and richer comprehension.  Logic mastery  improves reading and writing.  Logic mastery ease learning difficulties.  Logic mastery gives a headstart.  In sum, logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

After logic,   (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

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What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.

Try the Twiddla Whiteboard. In principle, it  allows to people to draw and chat together online on a copy of this webpage or a clean sheet. The chat may be via text or audio.  Visit www.twiddla.com to set up whiteboards to work with the webpage of your choice.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

Differentiation - The Quotient Rule

Quotient Rule: If

then 

Proof:  Observe

h(x) =

u(x)*

1   v(x)

Therefore the product rule and reciprocal rules imply

Reciprocal Rule Again: If

then 

One proof follow's from the Quotient Rule with u = u(x) = 1.

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More Calculus

Calculus Videos
0.   First Calculus Preview
0. Triangle Inequality
0 Inequalities
0. Solving Inequalities
1. Distance+Midpt Formulas
1. Function Domains
1.Polynomial Domain+Range
1. Fn:  Linear Combinations
1. Fn Composition II
1. Fn Composition I
1. Solving y**n = x**m
2 .Real Numbers
2. Limits Numerical View
2. Limits,. Formal Definition
2. Limit Properties Numerically
2. Decimal View of Limits
2. Error Control View
2. Limits & Continuity
2. Limit Vals via Substitution
2. Limits & Composite Fns
2.. Limit Examples
2. One Sided Limits
2. Infinity and Limits
2. Parameters in Limits
3. Derivative Motivation
3.  Derivative Definition I
3. Derivatives Definition II
3. Calculus: Why Radians
3 d/dx of sin(x) & cos(x)  (I)
3 d/dx of sin(x) & cos(x) (II)
3.Sum Rule
3. Product Rule
3. Power Rule
3. Previous Rules Combined
3. d/dx for Polynomials
3. Reciprocal Rule
3. Reciprocal Law: sec & csc
3. Reciprocals & Power Rule
3. Power Law for Integers < 0
3. Quotient Rule
3. Quotient Rule Examples
3. Quotient Rule: tan & cot
3.  Linear Chain Rule
3. Chain Rule for Powers
3. Chain Rule - Polynomials
3. Chain Rule Examples I
3. Chain Rule Examples II
3. Linear Approximation I
3. General Chain Rule
3. Inverse Fns Derivatives
3. Chain Rule: ln(x) & exp(x)
3. Square & Cube Roots
4.  Linear Approximation
4. Second Derivative Test
4. Sketch y = x^3 - 6x^2- 12x
4. Sketch y = x^3 - 3 x^2 - 9x
4. Sketch y = 1 - 1/(1+x^2)
5. Indefinite Integrals A
5. Indefinite Integrals B.
5  Indefinite Integrals C
6. Definite Integral D
6. Area Under Curves
7. Volume of a Sphere

To Learn More, visit Volumes 2 and 3.

Advanced Topics

Limit Properties Algebraically
Pigeon Hole Principle
Bolzano
Constant Difference Thm
Continuous Functions
Rational Functions
Mean Value Theorem
One Side Range Theorem
Range On One Side
From Lipschitz Continuity

To Learn More: Visit Real Analysis.

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