Talk:Calculus/More Differentiation Rules

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Contents

[edit] Order of TOC

I have noticed that the chain rule section comes before the product and quotient rule sections. I think that the quotient and product rule sections should come before the chain rule as the chain rule is more difficult than the other two. Evan W. 00:31, 7 June 2006 (UTC)

I agree. Rmbzz (talk) 01:14, 6 October 2008 (UTC)

[edit] product rule

is there any simple proofs that could be added to any of this? oh and is there a way to change the color of the font to highlight certin sections of a proof? good work I like what I've learned so far

one more thing could you explain this step more?

\frac{d}{dx} \left[ f(x) \cdot g(x) \right] = \lim_{h \to 0} \left[ g(x+h) \frac{ f(x+h) - f(x) }{h} + f(x) \frac{g(x+h) - g(x)}{h} \right]

Which, when we take the limit, turns into:

\frac{d}{dx} \left[ f(x) \cdot g(x) \right] = f'(x) \cdot g(x) + f(x) \cdot g'(x), or the mnemonic "one D-two plus two D-one"

Thanks for your time --Stranger104 10:57, 12 Jun 2005 (UTC)

I'm going to reword the discription of the chain Rule. its a little confusing as it is right now. oh I'm also having a hard time making f ' (X) look like its suposed to without spacing with the font thats being used in the explanation. any ideas how to fix this?--65.24.68.237 03:34, 13 Jun 2005 (UTC)

[edit] Implicit Differentiation

Does anyone feel that it would be a good idea to implement a section on implicit differentiation after the Chain Rule?

I decided to go ahead and add it. I hope it is clear and makes sense. Should I add more examples? -EbolaPox

[edit] revert vandalism

Just skimming through and spotted some vandalism so reverted but forgot to log in or leave comment duh?! i really need to go to bed 81.79.60.184 aka --SuperJ587 23:18, 9 June 2006 (UTC)

[edit] Reducing answers?

Shouldn't the answers to the exercises be reduced to the simplest terms?

For example, #4 answer is given as:

\frac{3x^2-6x^2-6x}{9x^4}

I think it should be reduced:

\frac{-3x^2-6x}{9x^4}
\frac{-3x(x+2)}{3x(3x^3)}
-\frac{x+2}{3x^3}

... but I'm not sure. I may have missed something.

That is correct.--Cronholm144 08:42, 18 June 2007 (UTC)

[edit] Euler's formula....

I don't think that throwing out Euler's formula is good pedagogy. Especially since Taylor series are required to establish that identity. Using the definition of derivative is far more informative for the aspiring student. --Cronholm144 08:33, 18 June 2007 (UTC)

Also the symmetric difference and the sinh(x) derivation is iffy. Are we assuming that reader is aware of hyperbolics? I have made quite a few edits, the page is rather different, please take a look.--Cronholm144 21:43, 18 June 2007 (UTC)

I removed the Euler's and I am going to rm the hyperbolic as well.--Cronholm144 02:06, 20 June 2007 (UTC)

[edit] Incorrect example

In the Quotient and Product Rules section, it gives an example of a function where the product rule is useful. The function contains both the pronumerals x and y, however the function is defined as H(x) and not H(x,y) and hence we differentiate only against x and not both x and y. When there is an unknown pronumeral that we are not differentiating against (y in this case) it is treated as a constant.--anon

I will take care of it--Cronholm144 01:57, 20 June 2007 (UTC)
Done--Cronholm144 02:05, 20 June 2007 (UTC)

[edit] Chain rule example error

Hey, I'm no math major, but shouldn't this eaxample in the chain rule:

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = 2u\cdot 2x = 2(x+5)(2x) = 4x^3 + 20

be corrected to:

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = 2u\cdot 2x = 2(x^2+5)(2x) = 4x^3 + 20x

—The preceding unsigned comment was added by 66.251.28.173 (talk • contribs) . (July 2007)

This was fixed in July 2007. --Mrwojo (talk) 01:46, 29 December 2008 (UTC)
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