# Tag: calculus

• ## Product rule

And here’s a quick recap of a demonstration of the product rule (after Leibniz): Which is, of course, the product rule.

• ## Integration by parts

Saw this referred to in A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity and it made me shudder – as I always seemed to struggle with it at ‘A’ level maths – so here, for my own benefit, is a quick proof/explanation of the method. The general rule…

• ## Euler’s formula proof

Reading An Introduction to Laplace Transforms and Fourier Series I reach the point where it is stated, rather axiomatically, that: . This is a beautiful formula and has always suggested to me some sort of mystical inner mathematical harmony (yes, I am a materialist, but I cannot help it). But these days I also want…

• ## Derivative of any number raised to the power of x

I know this is a piece of elementary calculus but I just worked it out from (more or less) first principles (as I knew what the answer was but did not know why). Let what is ? where is some constant. Hence or and so and so . And , so Applying the chain rule…

• ## Good maths or bad maths?

Not sure, so maybe someone who knows can tell me. Following on from the last blog, can we show ? Assume a constant, exists such that , could give us this ? Edit: Professor Rubin (see comments) tells me that, as I feared, what follows is not supportable: Now, and this is the bit I…

• ## Differential calculus reminder

This is just an online note to myself about differential calculus. A level maths again… Calculating where Using the chain rule: (as ) hence . So And , Euler’s number, really is magical. Related articles Using math symbols in wordpress pages and posts – LaTex (1) (etidhor.wordpress.com) Math it up. (ask.metafilter.com) When you get too…