Talk:Calculus/Derivatives of Exponential and Logarithm Functions

Calculus/L'Hôpital's rule is proposed to evaluate the $$\lim_{h \to 0} \frac{e^h - 1}{h}$$, however to use L'Hôpital's Rule one already needs to know how to compute the derivative of $$e^x$$ which we are trying to define here. It feels to me like a short circuit: we want to define the derivative of $$e^x$$, but then we need it's definition along the way to it's definition. Can someone, please, either comment on this or propose the other way to compute the limit? --137.248.153.117 (discuss) 17:40, 2 September 2014 (UTC)

Original definition of logarithm
Hyperbolic logarithm was developed in 1647 as quadrature of the hyperbola. Consider this source on derivating logarithm from a similar definition: It is suggested that this approach be added. Rgdboer (discuss • contribs) 05:04, 27 May 2020 (UTC)
 * Log as Integral.

Another source with the same approach to differentiating logarithm: The historic basis can be found at hyperbolic sector. Rgdboer (discuss • contribs) 19:42, 27 May 2020 (UTC)
 * Areas under a hyperbola and the logarithm

Evidently University of New South Wales and University of California, Davis have found it useful to expose students to hyperbola quadrature for calculus of logarithms. A page Calculus/Hyperbolic logarithm and angles has been added to this Wikibook to provide similar instruction. Rgdboer (discuss • contribs) 02:45, 16 June 2020 (UTC)