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#1 2012-11-20 23:35:45
- MathsIsFun
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- Registered: 2005-01-21
- Posts: 7,713
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2012-11-21 01:29:42
- Bob
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- Registered: 2010-06-20
- Posts: 10,621
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? 
Bob
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
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#4 2012-11-21 01:35:43
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
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#5 2012-11-21 02:34:45
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
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
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- Registered: 2010-06-20
- Posts: 10,621
Re: Derivative Rules
How is f'(sin(x)) the derivative of the sine function?
Where on the page did you find this, please?
Bob
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
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#7 2012-11-21 05:07:49
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
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#8 2012-11-21 05:13:28
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,621
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
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
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#9 2012-11-21 08:16:49
- MathsIsFun
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- Registered: 2005-01-21
- Posts: 7,713
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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