Timeline for what is the link between exponential/logarithmic function and 1/x
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 18, 2022 at 10:04 | vote | accept | Aminos | ||
| Jul 17, 2022 at 20:57 | answer | added | Victor Souza | timeline score: 2 | |
| Jul 16, 2022 at 22:54 | comment | added | Тyma Gaidash | It alludes to how $\sin(t)$ gives the arc length of a circle given an angle $t$, $\arcsin(x)$ gives the angle given the arc length x, and $\arcsin’(x)$ is the integrand. $\arcsin(x)$ can be put in terms of $\ln(x)$ while $\sin(x)$ can be put in terms of $e^x$. As for the intuitive explanation, $\int x^{-1} dx=\lim_{p\to0} \frac{x^p}p=\ln(x)$ | |
| Jul 16, 2022 at 22:41 | answer | added | Jean-Armand Moroni | timeline score: 2 | |
| S Jul 16, 2022 at 19:50 | history | suggested | bobeyt6 | CC BY-SA 4.0 | edited for latex |
| Jul 16, 2022 at 19:43 | comment | added | user2661923 | So, letting $y = e^x$, you have that $g(y) = x.$ Then $g'(y) = \dfrac{1}{f'(x)} = \dfrac{1}{f(x)} = \dfrac{1}{y}.$ Thus, the derivative of the function $g(y) = \ln(y)$ is $g'(y) = \dfrac{1}{y}.$ | |
| Jul 16, 2022 at 19:40 | comment | added | user2661923 | Posting this as a comment, rather than an answer, because my response is very informal, and not backed up by a solid understanding of the topic. The function $f(x) = e^x$ has the property that it is equal to its own derivative. That is, $f'(x) = f(x).$ Let $g(x) = \ln(x)$. Then $g(x)$ is the inverse function to $f(x)$. There is a principle in Real Analysis that when any $g(x)$ is the inverse of any $f(x)$, and when $f'(x_0) \neq 0$, then $g'(x_0) = \dfrac{1}{f'(x_0)}.$ ...see next comment | |
| Jul 16, 2022 at 19:13 | comment | added | bobeyt6 | Please use LaTeX and Mathjax formatting for future posts. | |
| Jul 16, 2022 at 19:13 | review | Suggested edits | |||
| S Jul 16, 2022 at 19:50 | |||||
| Jul 16, 2022 at 19:07 | review | Close votes | |||
| Jul 17, 2022 at 6:05 | |||||
| Jul 16, 2022 at 19:02 | history | edited | Aminos | CC BY-SA 4.0 | added 10 characters in body |
| S Jul 16, 2022 at 18:42 | review | First questions | |||
| Jul 16, 2022 at 18:43 | |||||
| S Jul 16, 2022 at 18:42 | history | asked | Aminos | CC BY-SA 4.0 |