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YOU are better than YOU think. Show yourself
how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence in
work
and study
Learn to read notes and textbooks like
a lawyer, so that no nuance, no subtlety and no clause escapes your
attention. |
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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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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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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 Product Rule
Product Rule: If g(x) = u(x)v(x) then g'(x) = u'(x)v(x) + u(x)v'(x)
[Play
Video] 2½ minutes: Product Rule for Differentiation,
indication of proof (why it holds). Proof is written below as well.
Proof:
Observe
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g(x+h)-g(x)
h |
= |
u(x+h)v(x+h) -u(x)v(x)
h |
|
|
|
= |
u(x+h)v(x+h) - u(x)v(x+h) + u(x)v(x+h) -
u(x)v(x)
h |
|
= |
u(x+h)v(x+h) - u(x)v(x+h)
h |
+ |
u(x)v(x+h) - u(x)v(x)
h |
|
= |
[u(x+h) - u(x)] v(x+h)
h |
+ |
u(x)[v(x+h) - v(x)]
h |
|
= |
u(x+h) - u(x)
h |
v(x+h) |
+ |
u(x) |
[v(x+h) - v(x)]
h |
Now taking the limit as h approaches zero implies the stated
rule: g'(x) = u'(x)v(x) + u(x)v'(x)
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