This week we learned many different things, including average speed, instantaneous speed, and derivatives. Who knew average speed actually meant slope. I have to admit i was a bit overwhelmed when we had to copy all of those derivative formulas down, but of course once we were taught what they were I felt much better.
The first thing we learned was average speed, and i'm pretty comfortable with that. What I am not comfortable with is instantaneous speed. I get the point and know the formula, but I get mixed up while plugging everything in..as in the example Find the instantaneous speed at t=2. y=16t2 as lim of h goes to 0. Since i have the notes on this problem, I can do it without a problem. But when I need to do a different problem without my notes, I get confused with what and where to plut into the formula as lim h goes to 0 f(x+h) - f(x) all over h. Everytime I work it i never get the right amount of h's in the end, and I get completely frustrated after that. I think I just need to practice more without getting frustrated, then I might get it. The other thing I don't always understand is the quotient rule. I know that the formula is vu1 - uv1 all over v2. All that means is copy bottom(derivative of top) - top(derivative of bottom) all over bottom squared. This is easy for me to explain but when simplifying I always try to cross out too much. I need someone to verify what I can and cannot cross out, or my whole answer is screwed up. One more thing I don't understand is when we have to find the derivative of a number raised to something then that is raised to something else. Example: x raised to pi squared. Do you just bring pi in front of x and subract one from pi like any other polynomial?
Well, atleast I understood something throughout the week in Calculus, better than nothing right? Now for what I AM comfortable doing. First, I finally get product rule. It's so simple, I don't understand why i never got it in the beginning. Simply put, it's copy top(derivative of bottom) + copy bottom(derivative of top). The only thing you need to remember is the different derivative formulas that will come up in the problems. Though the next thing I understood was completely easy and everyone understood it, it's still something so i'll say it anyway: derivatives of polynomials. If I had a test of just that, I may actually pass it.
Next week, I think i'll probably catch on a lot quicker. I was a little emotional and stressed out this week due to different reasons, but I'm better now so hopefully i'm ready even though we're moving on. We have a good class, and i think we're ready for whatever we are going to face.
Thank youuuu :)
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ReplyDeleteI think I can help you on that x raised to pi sqaured. You use the formula for exponents which is u^n = nu^n-1. So, you copy the exponent pi^2, then copy the base of that exponent which is x, and subtract one from your exponent. Your answer should be: (pi^2)x^(pi^2-1). It's kind of hard explaining it with words haha.
ReplyDeleteFor pluging into the instantneous speed formula you just have to be careful and double check to make sure what your plugging in is right. For the example in your notes, just plug in t everytime you see an x in the formula and after that is just algebra.
ReplyDeleteP.S. i also struggle with simplifying, you're not alone.