<p>So, my review book has tons and tons of different derivatives that it says you should memorize, but I'm curious to know how many of those are actually important to memorize. Do I really need to know the derivative of arcsin, or even simpler functions like sec^2?</p>
<p>I'm self teaching myself this exam, so I don't have much experience to go off of - I've only been doing this for a bout 5 days. Any help is appreciated! Thanks in advance!</p>
<p>From what I’ve noticed from all those practice tests, you should definitely know the derivatives of the trig functions, even the inverse ones, as well as the natural logs and e. The mean value theorem, related rates, and average rate of change also pop up frequently. It’d be best to fully understand velocity/acceleration/position, and where a function’s increasing/decreasing and concave up/down.
For the free response part, it’s like every year, there’ll be one question about the region between two functions. So for that, know how to do the washer and shell methods. Oh, and make sure you know how to find the volumes of cross-sections.</p>
<p>To be honest, the ones that you can derive yourself aren’t necessary, but for derivatives like d(logx)/dx, d(arcsinx)/dx and the sort that are too complicated or hard to derive in a short amount of time, I suggest you memorize them.</p>
<p>The important thing, though, is to not just memorize but to remember. Through practice you’ll pick up the key derivatives and by deriving them yourself you not only have a better time remembering them but also practice your differentiating skills. A few essential derivatives aren’t easy to derive so by actually doing so yourself, you will have developed an ability to derive harder functions that may actually appear on the test.</p>
<p>Know the theorems such as Mean Value, Intermediate Value, Extreme Value.
Know the derivative of a^x given that ‘a’ is a constant is ‘a^x lna’
I’ve seen problems that involve using the trig functions, sin^2x + cos^2x= 1</p>
<p>…ya just know everything</p>
<p>Mean Value Theorem of Derivatives
Mean Value Theorem of Integration
Reimann Sum (Left, Right, Midpoint)
Trapezoidal Rule</p>
<p>Derivatives of 6 trig functions
Product, Quotient, Chain Rule
Derivatives of (and therefore antiderivatives of the derivatives) …
arcsin, arccos, arctan
e^x (e^x)
log(base a)x (1 / xlna)
lnx (1/x)</p>
<p>Intermediate Value Theorem
Extreme Value Theorem</p>
<p>First Fundamental Theorem (duh, haha needed for a lot)
Second Fundamental Theorem (for when there is a variable in the interval)
Average Value
Area between two curves
Disc method
Washer method
Cross sections
Exponential growth and decay</p>
<p>And if you haven’t yet, learn…</p>
<p>critical points (f’(x) = 0 or undefined)
increasing (f’(x) > 0) and decreasing
maximum (f’(x) changes from negative to positive or f’‘(x)>0) and minimum
points of inflection (f’‘(x) = 0 or undefined and concavity changes)
concave up (f’'(x)>0) and concave down</p>
<p>What’s the extreme value theorem? o_O</p>
<p>Eta: Never mind</p>