Let's Differentiate BOB

It seems like I keep saying the same thing over and over again...It seems like I think I really get the concept, and then when we're supposed to apply it, I don't.

I understand how to find the related rates of sums, finding the approximations, which is kind of similar to the previous concept of Riemann sums, and I understand the laws that we've learned through the book. BUT the main thing for me, which makes everything go awry, is that I don't recognize the pattern, as Mr. K mentioned earlier. When it comes to solving a problem I have a hard time analyzing it and determining which rule or method to use. So that's something that could probably be solved with practice, which I tried by doing some exercises tonight, but honestly, it's not looking so good.

As well as that, one thing I'm still finding foggy is how to draw a derivative and how to determine which direction the function is growing... without using an actual function. I have a feeling I should know this by now, but I really don't know it to the core and I still have a lot of trouble with that. Also for some reason I really have trouble finding the derivative of a function the long way now, since I can't seem to get rid of the h in the general form of f ' (x) = f (x + h ) - f (x) / h

Because I don't quite know this, I feel... sort of.. left behind. But somehow I'll get there.. I hope.