I got bored several days ago and decided to relearn calculus.
I have been reading a book that I learned about from reading a post on the blog, God Plays Dice.
What is driving me crazy is how sloppy my arithmetic has become. I need sometimes 5-6 attempts at a problem to work through the basic mistakes and typos.
I am still deciding whether this is bad or good. Why good? Because the mistakes make me keep looking at the problem and understanding the concept I am being shown; bad because it reminds me how sloppy I have become.
Today though I have stumbled on a real mistake – an understanding mistake. I am trying to find the derivative of y = ((x)/4-x)) + (4-x/x).
Now I thought I could tackle this problem either using multiplication or division, but I get different answers. The ((x)/4-x))
side seems to want to derived by using only the ‘division method’ not the multiplication method. In my mind though they should be equivalent:
dy/dx = (x) (d(4-x^-1)/dy)) + (4-x) (dy x/dx) should be equivalent to dy/dx = ((4-x) (dy x/dx) – (x) (d(4-x^-1)/dy)))/ (4-x)^2.
Of cause I could be making an arithmetic mistake again! and yes I was making a stupid mistake!
Here is the original post and which has a link to the calculus book: Click.