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#1 2012-11-21 22:35:45

MathsIsFun
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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
 

#2 2012-11-21 22:57:44

bobbym
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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.
 

#3 2012-11-22 00:29:42

bob bundy
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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
 

#4 2012-11-22 00:35:43

anonimnystefy
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Re: Derivative Rules

Hi MIF

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#5 2012-11-22 01:34:45

ShivamS
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Re: Derivative Rules

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


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann
 

#6 2012-11-22 04:02:13

bob bundy
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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
 

#7 2012-11-22 04:07:49

anonimnystefy
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Re: Derivative Rules

Hi Bob

All of the examples contain that notation...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#8 2012-11-22 04:13:28

bob bundy
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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
 

#9 2012-11-22 07:16:49

MathsIsFun
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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
 

#10 2012-11-22 09:55:31

bobbym
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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.
 

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