d/dx between the two

Differentiate vs Derive
I think I've stated this before.
To differentiate is to find the gradient of a curve at a certain point by using the gradient formula and determining the gradient as the horizontal distance between your two reference points approaches 0. It is synonymous to "d/dx" (or whatever variable)
To derive is to obtain an expression or formula by reasoning and logical deduction. It is synonymous to "deduce", or in the mathematical context, "prove".
Reason for misconception: The product of differentiation is the derivative. It may be logical to think that the process is hence "deriving". But it's not, and you're wrong (Y)

Grammar vs Syntax vs Spelling
This stems from the fact that correcting spelling can get someone the label of a "grammar Nazi". Which is sadly misled.
Grammar is the set of rules for using a language. It is why we say "This is my phone" and not "This is I's phone". Strictly speaking, grammar is rigid and there is only "one right answer" - that is, there is only "one right grammar". Variations to grammar are wrong.
Syntax is the ordering of words in a sentence. It's the difference between "The ball was hit by the bat" and "The bat hit the ball". It's possible to play around with syntax and still have a legitimate English sentence.
Spelling is the ordering of letters to make an individual word.
I acknowledge there is overlap between syntax and grammar in that we are not meant to split the infinitive verb (e.g. "To angrily smash the ball" is wrong. It should be "To smash the ball angrily". I personally give zero craps about this rule and I am happy to rebelliously do what I want.)

Electric Shock vs Electrocute
Electric shock is when a sufficient current runs through a body part to cause any sort of undesirable effects.
Electrocuting is death by electricity. You have not been "electrocuted before".
Reason for misconception: It's gotta have something to do with electricity if there's "electro" in it, right?

Complimentary vs Complementary
Complimentary is usually used as an adjective to mean "free" or "gift" such as "complimentary breakfast at the hotel". Complementary is used to describe two or more objects that come together to make a recognisable set.

:/ vs :L
:/ is a worried face, like that face that absolutely nobody pulls when they're worried.
:L is actually a laughing face. That links to Bebo, the now tumbleweed social networking site that was pretty big before Facebook. If anybody will remember, that is where the ":L" shortcut started. If anyone was using it before Bebo got big at our school, I'd like to speak to you.
Reason for misconception: Taken at face (hoho) value, :L does indeed look like a sort of worried face. But it's kinda too ugly to be a worried face. Though to be fair, ugliness didn't stop people from using idiot emoticons like :F.

:) vs (:
"(:" is a backward smiley for backward people.


Okay time to whine about stuff that annoys me yay. Just tacking it onto the end of a post.
Laughing at someone
I believe A is being a total asshole if they are laughing at B and the following criteria are true.
1) A is not better than B at the skill.
2) There was no recent display of fail from B (e.g. if A is laughing B's skill in ball sports, in the middle of a maths period, where presumably B did not just fumble a ball and smack himself in the face)
3) B never claimed to be better than A at the skill.
4) If A didn't even claim to be good at the skill, and B just came out of nowhere.
Note that if 2), 3), or 4) were false, then it becomes acceptable to laugh. If 1) were false it doesn't qualify A to laugh, but if it were true it does make A more of an asshole. These are also cumulative. The more criteria someone satisfies the greater of an asshole they are. I was going to list some examples but I believe this is relatively clear - happy to provide examples on request.

The word "technically"
You cannot use the word "technically" in place of admitting being in the wrong. When people are (trying to be?) logical, and have their flaws exposed, I have oft hear them say "well technically..." to either mean "You're only right but by a technicality" or "Technically I'm right but you're right in every other way". No, mate, when you're resorting to idiot unfinished sentences like this you've fucking lost through and through. Take it graciously (I can't even say "like a man" any more) and admit defeat.
I was going to insert the Inigo Montoya meme but Meme Generator is down so whatevers.
Same goes for "probably...", "maybe..." and a shrug of the shoulders.

The misuse of scientific terms to sound cool
Okay like I look around and I see shit like Olay DNAge, "isoactive" toothpaste, and pop science buzzwords like "neutrino blasters" or "photon cannon" or "quantum anything"
1) You should be very fucking scared of anything that claims to "repair" or in any other way touch your DNA. Remember, that's how cancers are caused.
2) "Iso" means "equal". What the fuck is "equally active". Is it actually doing anything?!
3) Neutrinos are particles that have no charge and are tiny (iirc same size as electrons) and so they practically pass through everything unscathed. The Physics textbook says something like 10^13 neutrinos (from the Sun) are passing through you all the time, night or day, because even if it's at night time, those neutrinos can easily pass through the Earth. You ain't gonna hurt anyone by shooting neutrinos at them
4) A photon cannon would be a very bright light. By that logic a Maglite will be a photon pistol.
5) Quantum quite literally just means "discrete". And as far as I am aware, the significance of quanta is greatly reduced as soon as you stop considering the subatomic level, whereby all your "normal physics" (like that F=ma and v=f\lambda shit from year 9 and 10) can start applying quite happily. Also, quantum leaps in real physics are tiny ass leaps where matter seems to "teleport" small distances on the subatomic level. So a quantum leap in a spaceship would be rather unimpressive.

The assertion that writers and composers of other media "do not consider all these techniques"
"I swear the author wasn't thinking about this when he wrote this. Maybe he just wanted a cloudy day!!!"
I disagree wholeheartedly. Do you remember when you wrote your Belonging story? How many times did you stop to think what kind of atmosphere would be most conducive of belonging or lack thereof? Did you look back and go "wait how the fuck is anyone going to understand this" or "is there a better way to phrase this so that it seems like more of a shock" or "will the teacher spot my clever motif?".
Hell I know people who spent more than enough time choosing a goddamn name for their character.
And remember, we're all fucking scrubs when it comes to writing. Those people do it as their livelihood, and you're telling me they won't stop to consider what kind of effect each and every word will have on their readers?
With the exception of Fay Weldon of course. She just wrote whatever the fuck she felt like in the wake of Austen's success.
No but seriously, I bet even Weldon stopped to consider how well her work will convey her point. It's just not her fault she's not very good at it.