# Is this a bad habit? (1 Viewer)

#### HeroWise

##### Active Member
I have read that Delta x on Delta y is different to dx/dy

But im SOOO used to delta x/ delta y that when i do any questions i put it in. Is this technically wrong? or should i try to change this habit?

#### Drongoski

##### Well-Known Member
Didn't I already point out to you a few months ago that the 2 things are distinct. It is not just your bad habit (few people have this "habit") but it is simply incorrect.

And stop using delta y/delta x when you mean't dy/dx. Maybe most teachers and markers would overlook the difference; result is you think they are the same thing.

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#### HeroWise

##### Active Member
i do remember u pointing it out, and thanks a lot for it again,

but like i have heard in 4u the teacher basically forces you to use delta y on delta x

In school we just started basic integration as we are starting year 11 prelims next term. He has done dy/dx. I have seen that his methods pf teaching are actually good and an hsc marker, he do gives the expectations and standards for the hsc.
I addressed this because you told me off last time ahah
Im like in an inner battle rn
And again, when i started calculus, i used deltas so its like ingrained. need to really change it

and again thanks Drongoski

#### fan96

##### 617 pages
but like i have heard in 4u the teacher basically forces you to use delta y on delta x
Not true. If your teacher makes you do it then they are wrong.

In particular,

$\frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$

(as the Cambridge textbook states when introducing the derivative)

So the two are subtly different things - $\Delta y$ is a change in $y$, but $dy$ is specifically an infinitesimal change in $y$.

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#### Drongoski

##### Well-Known Member
i do remember u pointing it out, and thanks a lot for it again,

but like i have heard in 4u the teacher basically forces you to use delta y on delta x

In school we just started basic integration as we are starting year 11 prelims next term. He has done dy/dx. I have seen that his methods pf teaching are actually good and an hsc marker, he do gives the expectations and standards for the hsc.
I addressed this because you told me off last time ahah
Im like in an inner battle rn
And again, when i started calculus, i used deltas so its like ingrained. need to really change it

and again thanks Drongoski .
Please report such teachers to me for a public dressing-down.

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#### Drongoski

##### Well-Known Member
Not true. If your teacher makes you do it then they are wrong.

In particular,

$\frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$

(as the Cambridge textbook states when introducing the derivative)

So the two are subtly different things - $\Delta y$ is a change in $y$, but $dy$ is specifically an infinitesimal change in $y$.
What is "infinitesimal" (used a lot in textbooks in the 50's and prior) and how does it help clarify things? dy/dx is just the notation for the limit $\lim _{\delta x \to 0} \frac {\delta y}{\delta x}$ when this limit exists. This limit you now call the "derivative"; at one time it was also called the "differential coefficient"

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