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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Trying a new Introduction to Derivatives

Trying a new "Introduction to Derivatives": Introduction to Derivatives

(To replace this one: Introduction to Derivatives)

(Note: the next step will be a page describing how to use the rules like power rule, chain rule etc)

What do you think of the new one? Have I gone too far in simplifying? Any suggestions?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trying a new Introduction to Derivatives

Hi;

Like it as it is. It is clear and two examples are fine.

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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.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: Trying a new Introduction to Derivatives

Hi MathsIsFun,

The page Introduction to Derivatives is crystal clear. I don't think any further explanation is needed.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Trying a new Introduction to Derivatives

hi MathsIsFun

As ever, a great page.

Two suggestions:

(i) Make the diagram larger (see below).  The overlapping symbols make it a little confusing for a beginner.  I've taken the liberty of doctoring the diagram to show what I mean.  Really I would have liked to have a steeper curve, so that the points are more separated.

(ii) Rather than have the general rule first, then the examples afterwards, reverse this so that the reader gets to see some simple cases first, before learning the rule.

Hope that helps, 

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

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Trying a new Introduction to Derivatives

Thanks guys.

I have also opted for f'(x) rather than dy/dx ... what are your thoughts on that?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trying a new Introduction to Derivatives

Hi MathsIsFun;

dy/dx is better when you want to handle the derivative as a fraction by resorting to differentials. For everything else use f '(x).

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Trying a new Introduction to Derivatives

I would suggest both, as students will meet both.  You might consider a section entitled Two Notations.

I think dy/dx fits better with your explanation technique.

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: Trying a new Introduction to Derivatives

I would suggest both, as students will meet both.  You might consider a section entitled Two Notations.

I think dy/dx fits better with your explanation technique.

Bob

I concur with the views.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.