What is differentiation?

What are all the d's and what's lim?
Apart from knowing that it finds the gradient of a curve, i haven't a clue what it is.

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Reply 1

Mr. Orange

Differentiation is where you find the derivative :smile:

Reply 2

Mechie

Differentiation is a measure of the rate of change of a function. In a sentence.

Reply 3

Penguinsaysquack

When you differentiate, you find the rate of change of something, with respect to something else.
For lines on a graph, the rate of change of the line wrt x is the gradient..
In mechanics the rate of change of distance wrt time is velocity.
Make sense?

Reply 4

W.H.T

The opposite of integration

Reply 5

j.alexanderh

Original post by davidmarsh01

Differentiation is a measure of the rate of change of a function. In a sentence.

Like this. The d's (or deltas) mean 'very small change in', and the limit is the gradient of the curve of the function at a certain point. The limit is necessary as otherwise differentiation would involve division by zero, as you will no doubt learn when you do calculus.

Reply 6

Jake22

Differentiation is essentially about linear approximation of functions.

Reply 7

Farhan.Hanif93

Asking what differentiation is, is equivalent to asking what calculus is.

Reply 8

MUN123

It seems like Maths is not for me, because I just don't get the whole idea of defferentiation and Intergration. In my opinion both are useless and will not help me in the real world.

Reply 9

innerhollow

Asking what the "d" means is a tough question. The best way of thinking about it I think, is that

dx

refers to a TINY, TINY ("infinitesimal") change in

x

.

You know that the gradient of a straight line is found by

\frac{\Delta y}{\Delta x}

right? Can you see from this that

\frac{dy}{dx}

is exactly the same thing, just over a TINY, TINY range, as close to a single point as possible?

The limit basically means that

dx

gets as close to zero as possible without actually being zero (as you cannot divide by zero). It's a VERY abstract concept, but you'll be dealing with enough limits and asymptotic behaviour in A-level Maths that you should get used to the idea.

Original post by Farhan.Hanif93

Asking what differentiation is, is equivalent to asking what calculus is.

What is calculus? :cool:

(edited 13 years ago)

Reply 10

anshul95

To but it more intuitive way take the graph of x^2. I want to find the exact gradient at point x=1. First I draw a line between 0 and 1, and find the gradient of that line. Then draw another line between 0.5 and 1 find the gradient of this new line. The gradient of the new line is obviously a better estimate than the 1st line. Find the gradient of the line joining 0.9 and 1. This will close. Differentiation is the act of making the movable point closer and closer to 1, so that the gradient of the line becames closer to the exact gradient at x=1. That is why you use the lim notation - you are essentially taking a limit when following the above process. NB: There is a lot more to it e.g. formal definition of a limit, but I have told you the gist of it

Reply 11

Abused Tampon

Original post by innerhollow

What is calculus? :cool:

the same thing as diferention

Reply 12

kfkle

The derivative of a real-valued function

f

in a domain

D

is the Lagrangian section of the cotangent bundle

T^*(D)

that gives the connection form for the unique flat connection on the trivial

\boldsymbol R

-bundle

D \times \boldsymbol R

for which the graph of

f

is parallel.

:smile:

(edited 13 years ago)

Reply 13

markrush

Original post by MUN123

It seems like Maths is not for me, because I just don't get the whole idea of defferentiation and Intergration. In my opinion both are useless and will not help me in the real world.

Both may be useless to you but the people that use maths make pretty much everything you think are important to you in life. Finance, technology, even in farming complex maths is used for pricing and economics. To say it is useless to you maybe, if you meant in general :: shakes head ::.

As an aside true high end maths has a stunning beauty in logic and mystery. Geek moment over.

Original post by davidmarsh01

Differentiation is a measure of the rate of change of a function. In a sentence.

I was typing the exact same words, spot on.

Reply 14

Extricated

Its lyk timezin da co-efficient by da power and den minusing power by 1 innitttt

Reply 15

Raiden10

Original post by MUN123

It seems like Maths is not for me, because I just don't get the whole idea of defferentiation and Intergration. In my opinion both are useless and will not help me in the real world.

Seriously, just google "applications of calculus" just like you would google "football scores" or "angelina jolie" or whatever.

Be patient. It took people centuries to come up with this stuff, although the textbooks don't make it seem that way. As such, it's not surprising that it takes a few hours to understand. To be honest, I'm not sure I get the "whole idea" of differentiation and integration. It may not even exist. Calculus arose from practical concerns.

Reply 16

electriic_ink

Lim describes what happens to a function, f(x) as x gets close to a particular value eg:

\displaystyle{\lim_{x->12} (x+1)} = 13

because as x gets closer to 12, x+1 gets closer to 13.

\displaystyle{\lim_{x->2} \frac{1}{x-2}} = \infty

because as x gets close to 2, 1/(x-2) approaches infinity.

This one's a bit more interesting :p:

\displaystyle{\lim_{x->0} \frac{\sin x}{x}} = 1

(edited 13 years ago)

Reply 17

Makubex

I read the whole thread and after finish reading I came up with a conclusion that I didn't understand any of the above posts :s-smilie:

Reply 18

Evil Monkey

Original post by kfkle

The derivative of a real-valued function

f

in a domain

D

is the Lagrangian section of the cotangent bundle

T^*(D)

that gives the connection form for the unique flat connection on the trivial

\boldsymbol R

-bundle

D \times \boldsymbol R

for which the graph of

f

is parallel.

:smile:

Awwh that's so cute, you actually think you're smart just because you can throw some more technical words in to confuse the OP!

He never even asked about keeping it real valued. Maybe if he had it'd give him something a bit more to look at, but it's actually completely useless in every way. Every other answer, that just tries to be helpful instead, works regardless of where you're applying it. So really, I would love to be wrong, what were you trying to do here...