Hi, I was wondering about one of the calculations in this question. I saw that x times the derivative of 10/(1-x^2) was x(-2x*10)/(1-x^2)^2, but shouldn’t the numerator be positive for that calculation, or am I missing a concept here? Thanks
Hi,
I am not sure what you mean that the numerator should be positive.
The condition number should be positive, and it is | -2x^2/(1-x^2) |.
When studying it, you can study what is inside the abs value.
When that goes to ±Inf, then kappa goes to +Inf, and there is ill-conditioning.
Are you asking about this or something else?
This gives me the opportunity to mention that you should not be using automated software/etc to calculate derivatives.
You should be able to differentiate functions by hand.
Oh okay thanks, I think I understand that, I was just wondering about the calculation that resulted in the minus sign in front of the 2x*10 (at the top). I realize now that it doesn’t matter because of the absolute value around the entire fraction, but I had done the calculations on paper beforehand and did not get that minus sign, so I was just wondering if I had made an error, so I checked it using an online tool and got the same answer I calculated. This led me to wonder if I had made some sort of conceptual misunderstanding if even using an online tool resulted in me getting a different answer from the slides.
Thanks