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#1 2012-11-20 23:35:45

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Derivative Rules

Made a page on Derivative Rules

Lots of examples, possible errors (let me know!)

Also if you have any bright ideas on how to make it better.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2012-11-20 23:57:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,538

Re: Derivative Rules

Hi;

I did not find any errors in the examples. Looks good from here.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2012-11-21 01:29:42

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Derivative Rules

hi MathsIsFun


Very good.  I have the following suggestions (in red.... I seem to have lost the super and subscripts.) :

(1)     Derivative Rules

Logarithms        loga x            1 / (ln a)x     1/(xln a)

(2)    Example: What is (sin(x2))' ?
sin(x2) is made up of sin() and x2:
•    f(x) = sin(x)     f(g) = sin(g)
•    g(x) = x2
(3)    Example: What is (1/sin(x))’ ?
1/sin(x) is made up of 1/x and sin():
•    f(x) = 1/x     f(g) = 1/g
•    g(x) = sin(x)

What do you think?  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2012-11-21 01:35:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,385

Re: Derivative Rules

Hi MIF

How is f'(sin(x)) the derivative of the sine function?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2012-11-21 02:34:45

ShivamS
Member
Registered: 2011-02-07
Posts: 3,518

Re: Derivative Rules

Stefy, why is it not? Anyways, it is a very well-developed page. Perhaps you should add an video?

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#6 2012-11-21 05:02:13

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Derivative Rules

Stefy wrote:

How is f'(sin(x)) the derivative of the sine function?

Where on the page did you find this, please?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2012-11-21 05:07:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,385

Re: Derivative Rules

Hi Bob

All of the examples contain that notation...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2012-11-21 05:13:28

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Derivative Rules

Oh I see.  It's the notation that you were asking about.

Some people use f' for df/dx

The double diff is f''

etc etc.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2012-11-21 08:16:49

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Derivative Rules

I like f' because it is short and sweet. But dy/dx has the advantage of saying you are differentiating with respect to x.

Bob: thank you, those changes will make it better for sure!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2012-11-21 10:55:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,538

Re: Derivative Rules

Hi MIF;

The tables you put in tend to make everything too easy. A few of them I did not even know! Had to derive them by the chain rule to convince myself they were true. Can't wait to see your page on the chain rule!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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