Week #1

First week of Calculus finally done and with little blood shed. After hours of doing Calculus homework and helping people with Calculus, I notice that some people did not understand some questions on the first packet. An example question: "Supposed w'(-1)=18 and w(-1)=0. Find g(-1) assuming (wg)'(-1)=32." After staring at it for a good 10 minutes I finally understood it.

First off, you should recognize that they are using the product rule (uv)'=u(v') + v(u'). (w=u and g=v)

Secondly, if they -1 is confusing anyone just ignore it because they all plug -1 in for x, meaning that they are all the same.

To start this problem, write out the fully expanded product rule. Then, just start plugging in numbers where they belong. You should get (0)(g') + (g)(18)=36. Simplify the problem, which leaves you with 18g=36. Just divide 36 by 18 you find that g(-1)=2.

This also applies to problems that use the quotient rule also, so do not be scared because it turns out to be relatively simple.

One thing I really did not grasp until recently, though, was being able to manipulate the problem algebraically before taking the derivate. A good example of this is -2/(x^3). Besides the fact that it is still a simple problem, you can really save time by just moving the x^3 up, giving you -2(x^(-3)), which makes it much easier that doing the quotient rule. This little trick can save you a lot of time on any test, including an ACT or Mu Alpha Theta competition test.

Another little side note...If you understand derivatives and want to start trying to gain speed while doing them, stop and make sure you do the math correctly first because if your going too fast to realize that you did not subtract your fractional exponents correctly, you will have to go back and redo half of the problem or just not notice and get all of the problems wrong.