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Quick A Level Maths lesson.

(Pronounced as 'diff - er - en - she - ate', or 'diff - er - en - chee - ate') Differentiating is this -

Part 1: Start with the expression [a * x ^(b)] or 'A times X to the power of B',

This means that

you [multiply x by itself b times].

(an example is [x^3] would be [x times x times x].

Speak it as 'X to the power three', or 'X cubed')

Multiply a (the 'coefficient')

by x (the 'variable')

Part 2: To differentiate,

you take the power - 'b' in this example - and multiply it by the term -

Where 'term' means an individual chunk

(ab + bc means add chunk 'ab' to chunk 'bc' and therefore there are two chunks, or terms, in this example)

Written out, our starting expression, b times the original would become b * [a * x^b], spoken 'B times A times X to the power B'

Finally, you subtract 1 from the power. so b * [a * x^b] ends up b * [a * x^(b - 1)], spoken as 'B times A times X to the power B minus one'.

To simplify this into its shortest densest presentation, remove unnecessary operations (addition, subtraction, multiplication, division - where you perform an operation on a term. To operate means to complete a contextually agreed change to the previous and following terms)

(But this is not even my final form, Ichigo or other anime protagonist inexplicably powered by friendship and human social structures!!)

abx^(b-1) or bax^(b-1) is.

- since a * b, ab, or 'a times b', and b * a, ba, or 'b times a' both produce the same answer.

In fancy speak, they are 'commutative' or they 'commute'.

The commutation isn't a huge detail, until you get into weird shit like quantum mechanics and different number systems. Then, basically, ab and ba stop meaning the same thing and produce different results. Fuckin' weird, right??

Altho, it's like how when walking down a street and turning [left then right] can lead you somewhere completely different from the same street and turning [right then left].

In this case, you'd be performing function

TurnLeft([street start]) then TurnRight([street middle]) - compiled as TurnRight( TurnLeft([street start]) ) -

versus

TurnRight(start) then TurnLeft(middle) to be TurnLeft( TurnRight(start) )

BODMAS or Order of Operations are key to all of this. When in doubt, use parentheses when solving or practicing. This keeps your working out clear and makes error-checking more efficient!

(Pronounced as 'diff - er - en - she - ate', or 'diff - er - en - chee - ate') Differentiating is this -

Part 1: Start with the expression [a * x ^(b)] or 'A times X to the power of B',

This means that

**after**you [multiply x by itself b times].

(an example is [x^3] would be [x times x times x].

Speak it as 'X to the power three', or 'X cubed')

Multiply a (the 'coefficient')

by x (the 'variable')

Part 2: To differentiate,

you take the power - 'b' in this example - and multiply it by the term -

Where 'term' means an individual chunk

(ab + bc means add chunk 'ab' to chunk 'bc' and therefore there are two chunks, or terms, in this example)

Written out, our starting expression, b times the original would become b * [a * x^b], spoken 'B times A times X to the power B'

Finally, you subtract 1 from the power. so b * [a * x^b] ends up b * [a * x^(b - 1)], spoken as 'B times A times X to the power B minus one'.

To simplify this into its shortest densest presentation, remove unnecessary operations (addition, subtraction, multiplication, division - where you perform an operation on a term. To operate means to complete a contextually agreed change to the previous and following terms)

(But this is not even my final form, Ichigo or other anime protagonist inexplicably powered by friendship and human social structures!!)

abx^(b-1) or bax^(b-1) is.

- since a * b, ab, or 'a times b', and b * a, ba, or 'b times a' both produce the same answer.

In fancy speak, they are 'commutative' or they 'commute'.

The commutation isn't a huge detail, until you get into weird shit like quantum mechanics and different number systems. Then, basically, ab and ba stop meaning the same thing and produce different results. Fuckin' weird, right??

Altho, it's like how when walking down a street and turning [left then right] can lead you somewhere completely different from the same street and turning [right then left].

In this case, you'd be performing function

TurnLeft([street start]) then TurnRight([street middle]) - compiled as TurnRight( TurnLeft([street start]) ) -

versus

TurnRight(start) then TurnLeft(middle) to be TurnLeft( TurnRight(start) )

BODMAS or Order of Operations are key to all of this. When in doubt, use parentheses when solving or practicing. This keeps your working out clear and makes error-checking more efficient!

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Advanced, but if you're up for it: go for it

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Sounds like CBT / REBT

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The physics of physics

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Mathy math math. I can manipulate it, but for physics. I'm not a mathematician (yet)

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Google scholar is a thing, lots of schools have membership to online databases, and libraries have collections of magazines and newspapers.

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