The integral formula for secant is often introduced in a very artificial way. In this post, I look at the history of this integral and give several derivations.
In differential calculus, the product rule is both simple in form and high in utility. As such, it is typically presented early on in calculus courses, and the proof given is almost always the same.
In this post, we’ll explore the merits of a second proof of the product rule using properties of the logarithm, one that I hope presents a motivated and compelling argument as to why the product rule should look the way it does.