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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

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
Administrator
Registered: 2010-06-20
Posts: 10,053

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


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 smile

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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
Administrator
Registered: 2010-06-20
Posts: 10,053

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


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 smile

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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: 10,053

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 smile

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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

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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