How did I miss this easy derivative question on my calc 2 exam?

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Discussion Overview

The discussion revolves around a participant's experience of missing a derivative question on a calculus exam, leading to reflections on exam strategies and the challenges of understanding derivatives involving variable exponents. The scope includes personal anecdotes, exam techniques, and the emotional impact of exam performance.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related
  • Meta-discussion

Main Points Raised

  • One participant expresses frustration over missing a derivative question, highlighting the difficulty of the problem and their prior success in math.
  • Some participants suggest using the chain rule and power rule for the derivative, while noting the complexity of the expression.
  • Several participants share their own experiences of making similar mistakes in exams, emphasizing that such errors are common and not indicative of one's overall abilities.
  • Discussion includes various exam strategies, such as skipping difficult questions initially to manage time and anxiety during tests.
  • There is humor about the variable 'x' being a source of frustration, with participants joking about its role in equations and exams.

Areas of Agreement / Disagreement

Participants generally agree that mistakes in exams are common and share similar experiences, but there is no consensus on the best approach to handling difficult questions during exams. Various strategies are proposed, but no single method is universally accepted.

Contextual Notes

Some participants mention specific techniques for managing time and anxiety during exams, but these strategies may depend on individual preferences and the nature of the exam. The discussion reflects a range of experiences and opinions without resolving the effectiveness of any particular approach.

Who May Find This Useful

This discussion may be useful for students in mathematics or related fields who are preparing for exams and looking for strategies to manage exam stress and improve performance on derivative-related questions.

octahedron
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So in a calc 2 exam, you gloss over all the derivatives questions and get to integration and series. You get the really tough integrals, but you miss the grade-boosting derivative question (10%/100)?! So I've never gotten lower than 95% on a math midterm, but now I'm getting 85%~. Look at how stupid I was when I saw this question:

Find y' of (x^{2} + 3x)^{ln(x)}. If I told you I used power rule, how'd that bode for me as a math major?
 
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Art is a nice major :smile: - not meant to denigrate Art...
 
That's not an easy derivative. Should of used the chain rule first though, then it looks like some sort of product, I had a quick go, but I think it might take a while. And anyway quit beating yourself up everyone makes mistakes. :smile:
 
Oh, I used the chain rule along with the power rule. My point was that I treated ln(x) as a constant by somehow overlooking the x in ln, ha ha. Definitely looking at art history for a change.
 
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octahedron said:
Oh, I used the chain rule along with the power rule. My point was that I treated ln(x) as a constant by somehow overlooking the x in ln, ha ha. Definitely looking at art history for a change.

Hehe, yeah that's pretty dumb, but nobody's perfect. :smile:

The power rule is the chain rule for powers, I got what you meant.

Oh by the way x is not a constant. :-p
 
x is a constant pain in the ass. I'm always having to solve for x. Why can't x solve for itself?
 
octahedron said:
So in a calc 2 exam, you gloss over all the derivatives questions and get to integration and series. You get the really tough integrals, but you miss the grade-boosting derivative question (10%/100)?! So I've never gotten lower than 95% on a math midterm, but now I'm getting 85%~. Look at how stupid I was when I saw this question:

Find y' of (x^{2} + 3x)^{ln(x)}. If I told you I used power rule, how'd that bode for me as a math major?
Don't take it so hard. In cases like this, I have just worked out the problem and shown it to the teacher so that the teacher realizes I know how to work the problem. I'm sure I've made exactly the same mistake with regard to a variable exponent.

Sometimes one has to think in terms of f(x)g(x).
 
Astronuc said:
Sometimes one has to think in terms of f(x)g(x).

Then one just has to remember that

<br /> f(x)^{g(x)} = \exp(g(x)\ln(f(x)))<br />
 
sometimes, one of the techniques which I utliize whenever I take exams is this:

Skip over any questions which you have to think for more than about 1-2 mins. This ensures that you do not spend needless time over questions that you MAY not be able to solve. Instread, when you get back to these questions, you should have plenty of time to solve them and this psychological advantage will help you calm your nerves whereas if you were to solve the question head on, you will get more nervous as you feel that you are running out of time and spending too much time on one question.
 
  • #10
My anxiety levels in exams were terrible (as they are everywhere). I used to go in rush as much as I could in the 30 minutes and then run away :smile:. I'm amazed I passed anything.
 
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  • #11
Oerg said:
sometimes, one of the techniques which I utliize whenever I take exams is this:

Skip over any questions which you have to think for more than about 1-2 mins. This ensures that you do not spend needless time over questions that you MAY not be able to solve. Instread, when you get back to these questions, you should have plenty of time to solve them and this psychological advantage will help you calm your nerves whereas if you were to solve the question head on, you will get more nervous as you feel that you are running out of time and spending too much time on one question.

Excellent test strategy. It's a confidence booster to get two or three easy problems done, then you can relax and concentrate on the rest of the exam.
 
  • #12
Oerg said:
Skip over any questions which you have to think for more than about 1-2 mins. .

I did that to my electormagnetism exam. I ended up just skipping all problems, and just started over again...
 
  • #13
tkjacobsen said:
I did that to my electormagnetism exam. I ended up just skipping all problems, and just started over again...

:smile:
 
  • #14
Laugh if you will, I did the exact same thing on more than one occasion.

Last test, there were only 3 problems.
 
  • #15
Oh I remember those days very clearly. There aren't any "gimmees" on upper division E&M exams!
 
  • #16
Kurdt said:
x is a constant pain in the ass. I'm always having to solve for x. Why can't x solve for itself?
Yeah, what a useless variable. It should start pulling its own weight and solving some of its own problems. :rolleyes:

tkjacobsen said:
I did that to my electormagnetism exam. I ended up just skipping all problems, and just started over again...

:smile: Indeed, that advice only works up to a certain level. When you get 6 questions and 4 hours for an exam, skipping the hard questions while looking for some you can quickly complete in 1-2 min isn't a very effective strategy anymore. :biggrin:

octahedron, there's no point beating yourself up over it. Everyone has made a fatal exam mistake that lost them a lot of points for reading carelessly at sometime in their life.
 
  • #17
I'm definitely not beating myself over this again. :p
Oerg said:
Skip over any questions which you have to think for more than about 1-2 mins.

I did that in my physics midterm (baby E&M), and it served me well. Somehow during my math midterms I get too excited for my own good and decide to get to the "real" questions quickly and skip all the fluff (the derivatives -- two of them, and accounting for 20% -- were fluff, but I somehow regret not second guessing myself on the second one -- it seemed over too quickly).

tkjacobsen said:
I did that to my electormagnetism exam. I ended up just skipping all problems, and just started over again...

Heh. Sorry about that.

Kurdt said:
x is a constant pain in the ass. I'm always having to solve for x. Why can't x solve for itself?

I know, right? Found the pun funny, ha ha.
 
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  • #18
octahedron said:
Heh. Sorry about that.

Don't be, I got an A :smile:
 

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