Difference between differential and derivative

[conjecture]

I want to know the difference between the following pair of words:

(1) Differential vs. Derivative

(2) Differentiable vs. Derivable

I find both types of terms occuring in the book and I am beginning to
doubt whether they are same or they have different meanings.

[se...@btinternet.com]

On 27 Jul, 07:33, conjecture <my.conject...@gmail.com> wrote:
> I want to know the difference between the following pair of words:
>
> (1) Differential vs. Derivative

They both have multiple meanings, but in basic calculus they are
similar and it would be worth reading
http://en.wikipedia.org/wiki/Derivative
http://en.wikipedia.org/wiki/Differential_%28calculus%29

The usual noun is "derivative" in the sense of dy/dx or f'(x). Some
people might use "differential" for dy.

>
> (2) Differentiable vs. Derivable
>

"Differentiable" and "differentiate" are the usual adjective and verb
in calculus. Derivable means capable of being derived, and usually
means inferable or deducible from the original premise(s).

[Joshua Cranmer]

conjecture wrote:
> I want to know the difference between the following pair of words:
>
> (1) Differential vs. Derivative

The derivative is the change of a function with respect to one of its
variables, commonly denoted by the notation D_x, d/dx, dy/dx or f'(x)..

A differential is a variable (dx is the only common notation I've seen)
that represents an "arbitrarily small" change. A derivative can be
viewed as the division of two differentials.

> (2) Differentiable vs. Derivable

A function is differentiable iff it is a derivative (non-precise terms).

Derivable means "able to be derived", which means that it (ambiguous
antecedent by necessity) can be proven using a series of formal proof steps.

[fjb...@yahoo.com]

On Jul 27, 12:23 pm, Joshua Cranmer <Pidgeo...@gmail.com> wrote:

> conjecture wrote:
> > (2) Differentiable vs. Derivable
>
> A function is differentiable iff it is a derivative (non-precise terms).

"*Has* a derivative", I'm sure you mean.

[oliverm...@gmail.com]

For instance y=2x + 3 , two variables are involved. measuring the changes occurring in a variable is the differential like change in x (dx) whilst comparing the changes occurring in both variables is the derivative (dy/dx)

[John Gabriel]

All the responses you received are bullshit. Here is your answer from a real mathematician:

1. A differential is a finite difference of a given variable such as x, y, z, t, etc. Example: y=x^2. dy/dx = 4x / 2 means dy is equal (=) or proportional (~) to 4x, and dx is =~ 2.

2. A derivative is the ratio of two differentials. See previous example.

3. The only time a derivative is a rate of change is if one or more of the differentials are time differentials.

This is EXACTLY what a differential and derivative are. There is no bullshit about infinitesimal nonsense, limits or infinity. A derivative is EXACTLY a symbolic fraction.

http://thenewcalculus.weebly.com

[John Gabriel]

On Monday, 28 July 2008 03:23:30 UTC+8, Joshua Cranmer wrote:
> conjecture wrote:
> > I want to know the difference between the following pair of words:
> >
> > (1) Differential vs. Derivative
>
> The derivative is the change of a function with respect to one of its
> variables, commonly denoted by the notation D_x, d/dx, dy/dx or f'(x)..

Bollocks. There is NO change of any kind taking place. That fallacy was propagated by highly stupid academics who never understood calculus and never will.

>
> A differential is a variable (dx is the only common notation I've seen)
> that represents an "arbitrarily small" change. A derivative can be
> viewed as the division of two differentials.

A derivative IS the ratio of two differentials. Nothing else.

>
> > (2) Differentiable vs. Derivable
>
> A function is differentiable iff it is a derivative (non-precise terms).
>
> Derivable means "able to be derived", which means that it (ambiguous
> antecedent by necessity) can be proven using a series of formal proof steps.

You are an ignoramus. There is nothing arbitrarily small involved. That's typical mainstream mythmatics nonsense you have been brainwashed with.

[John Gabriel]

On Sunday, 27 July 2008 14:33:23 UTC+8, conjecture wrote:

Forgot to answer the last question:

What does differentiable at a point mean?

It means that only ONE tangent line with a defined gradient can be constructed at that point. It is the tangent line which tells us whether or not a curve is smooth, provided it is continuous.

Mainstream fools talk about differentiability at a point, but in fact, this is a stupid approach, because in order to be differentiable at a point, a function MUST be differentiable on the small interval containing the point. Fucking mainstream morons who should never have been allowed to have anything to do with mathematics have obfuscated these concepts because they have NEVER understood them. Surprising? Not when you consider the idiot Cauchy who defined the derivative as follows:

"A derivative exists at point p, if and only if, a derivative exists for every point in the interval containing p, except perhaps at p."

Study the flawed definition: f'(x)= lim (h->0) {f(x+h)-f(x)}/h and you might see that what I am telling you is true.

For the first and only rigorous formulation of calculus in human history, visit:

http://thenewcalculus.weebly.com

You won't learn any math here. Only mythmatics.