I know I should know this, but I can’t get my head around it. Let’s start with:
1/1/2. Simple - one takes the reciprocal of 1/2, so it is 1*2/1=2.
Okay, but the worksheet I’m going over for calculating derivatives asks to figure out the derivative of f(x)=1/(x-1) from first principle.
So I get this far:
the limit as h approaches 0 of -h/(x+h-1)(x-1)/h. OK, so if 1/1/2 is 1*2/1, why aren’t we taking the reciprocal of (x+h-1)(x-1)/h and coming up with -h(h)/(x+h-1)(x-1). The next step of course is -h/h(x+h-1)(x-1), the h’s cancel out, and you get a cromulent derivative.
As always, not homework - just an old guy trying to come to terms with the math he glossed over in his youth.