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Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

differentiation

if we differentiate on y with respect of x so.dy divide by dx why we could not differentiate ???

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: differentiation

Hi;

Got an example of what you mean?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

dy/dx why we cannot work.further

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: differentiation

That is the Leibniz notation for differentiation. When you say work further what do you mean?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: differentiation

That is the Leibniz notation for differentiation. When you say work further what do you mean?

I think he assumes dy and dx to be different expressions, and he is asking why can't we simplify dy/dx --> y/x? We do not treat them as different expressions,

Last edited by Mathegocart (2016-07-28 01:12:53)

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

Yes and why limit delta x approach to zero delta y/delta x why it is equal to dy /dx

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: differentiation

There is a good introduction to differentiation here:

http://www.mathsisfun.com/calculus/deri … ction.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: differentiation

Check out the link bob bundy posted, that should hopefully answer most of your questions. However, as Spivak asserts in Calculus on Manifolds, notation such as

and

by themselves is a bit of a touchy subject, because they often carry numerous different definitions depending on the author and are almost always done so that the equation

works out. Further, if

then classically we define:

(whatever

and

mean)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: differentiation

Hi zetafunc,
You are making it more difficult for him.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: differentiation

Hi Zeeshan 01;

Figured it out?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

if there is dxy\dx why we not apply.cu rule because y is consider constant with respect to x   
if we take another.example
dax/dx in this example why we consider a constant

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Malik

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: differentiation

if there is dxy\dx why we not apply.cu rule because y is consider constant with respect to x   
if we take another.example
dax/dx in this example why we consider a constant

Do you mean

and

?

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

yes

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

i am saying in your first statement why we apply uv rule and not cu because y is constant if we take.with respect to.x

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Malik

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: differentiation

can be considered as a constant if you want it to be -- it depends on if it is a constant in the function you're trying to differentiate. If it is, then:

The same holds true if

is a constant. If it isn't, then you should use the "uv rule" (which is normally called the "product rule"). For instance,

could be a function of

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: differentiation

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

why y is not constant if dxy\dx

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Malik

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: differentiation

why y is not constant if dxy\dx

We hold both of them constant.

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

how y is function please give example

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: differentiation

when we apply uv rule

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Malik