Post 30

This week we took a few more aps. I must say I'm getting better at them. I do well on the non-calculator portion just because every week we only have time to really thoroughly go through the non-calculator portion. I may start switching it up.

Anyway, last week on the aps we had problems like taking th ederivative of a natural log, chain rule derivatives, mean value theorem, and more integration I didn't know could be done using substitution.

Ok, for taking the derivative of a natural log, it's actually really simple. At the beginning of the year, B-rob gave us a sheet that showed the derivatives of everything that could be derived and natural logs were of course on there. Troughout the time from then to now, I guess I forgot how to do it and though tit was really hard, but it actually isn't. All it is is 1/x

For example:

d/dx ln(ln(2 - cos(x)))

For this one, you are basically doing a chain rule with a natural log. With chain rules, you are to always start with the outside of the problem and work your way in, taking the derivative of each term. So this would start off as

l/ln(2 - cos(x))

Then you'd have to multiply by the derivative of the inside which would be

1/ln(2 - cos(x)) X 1/(2 - cos(x)) X sin (x)

Giving you

sin(x)/(2 - cos(x)) ln(2 - cos(x))

For the mean value theorem, I used to forget to set it equal to the derivative, but the formula is

f(b) - f(a)/b - a = f '(x)

Ok, some things I"m haveing problems with:

Last week on the ap, they asked to give the derivative of f^-1 and saying that the problem is invertible. I really don't know what this means, so I tried to just put 1/the function and take the derivitave in that way, but I never get an answer.

Also, I'm having problems with piecewise functions and rate of change problems
Help please!