Hawthorne - I removed the note because ex is defined for all complex numbers, and so is ln(x). (See, for example, Euler's formula.)
- Fair enough. Maybe someone cleverer than us both can find a way to make it both simple and precise.
Also, I think that there are a lot of people unfamiliar with the universal operator, and it makes the formula overly confusing. I really don't think one needs to be that precise for something that goes without saying, especially when it obscures the simplicity of the concept.
- you mean the ? Perhaps so - how about we replace it with good old fashioned English instead.
Perhaps the set operators can be separated from the main formula? Perhaps that part (along with the right and left inverse) can have it's own small section on the page? I think this would improve the page.
-User:Kevin_baas 2003.06.24
- The right and left inverse could be separated off if neccessary, although I think if care is taken with wording that stuff can be made to fit in here without making the page any harder to read. However the definition of inverse must include the composition both ways around. Otherwise it just isn't right.
- Yes, it must, I know.
- I think that the switch to English helped alot. I concede on the right and left inverse on account of this.
-User:Kevin_baas 2003.06.24
For example, x3 + x, at x = 2, equals 10; the inverse function equals 2, when x = 10. If one tries to find the derivative of f(x)−1, at x = 10, one might note that f ' −1(10) = 1 / f '[f −1(10)] = 1 / f '(2); and since f ' is 3x2 + 1; then, f ' −1(10) = 1 / [3(2)2 + 1] = 1 / 13. Indeed, f '(2) = 13; thus f '−1 should be 1 / 13.
Is this not correct? Pizza Puzzle
Do you calculate (f(x)−1)' or f−1(x)'? Your calculation is correct if it is the second case. Wshun
Well, Im not sure I understand your question; but, if this is correct, perhaps it should be reinserted to the article? Pizza Puzzle
The first symbol (f(x)−1)' means ((1/f(x))−1)' which equals -f '(x)/(f(x))2, not 1/f '(x). It seems that you are confused the symbol of pointwise inverse f(x)−1=1/f(x) with the symbol of inverse function f−1(x) Wshun.
Yes, but barring that issue (which can be easily corrected) is there any reason to exclude this example from the text? Pizza Puzzle
- The differentation section currently is missing examples. It would probably do good for it to have an example section with at least one example. -- Provided that the example is appropriate, uses the correct notation, and is clearly presented( i.e. inline formulas = bad, the steps are clearly shown, the example is simple and fundamental, the structure of the presentation is visually clear, ect.).
User:Kevin_baas 2003.06.26
For example, x3 + x, at x = 2, equals 10; the inverse function equals 2, when x = 10. If one tries to find the derivative of f(x)−1=1/f(x), at x = 10, one might note that f ' −1(10) = 1 / f '[f −1(10)] = 1 / f '(2); and since f ' is 3x2 + 1; then, f ' −1(10) = 1 / [3(2)2 + 1] = 1 / 13. Indeed, f '(2) = 13; thus f '−1 should be 1 / 13.
Any other corrections desired? Pizza Puzzle
Hawthorne- I really don't think that adds to it. What you did is:
1. make a sentence more complex
2. added new concepts into the mix which are
- a. unneccessary
- b. not defined on the page
3. put an example
- a. outside the example section
- b. before the definition
I think that it's important to first get the main concept across as quickly and directly as possible, and develop the detail and specifics afterwards.
-User:Kevin_baas 2003.06.26
For example, x3 + x, at x = 2, equals 10; the inverse function equals 2, when x = 10. If one tries to find the derivative of f(x)−1=1/f(x), at x = 10, one might note that f ' −1(10) = 1 / f '[f −1(10)] = 1 / f '(2); and since f ' is 3x2 + 1; then, f ' −1(10) = 1 / [3(2)2 + 1] = 1 / 13. Indeed, f '(2) = 13; thus f '−1 should be 1 / 13.
Any other corrections desired?