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Math Help - simplifying a derivative

  1. #1
    No one in Particular VonNemo19's Avatar
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    simplifying a derivative

    find the derivative:

    x^2sinx

    This is one of my homework problems and It says simplify the result

    is x^2cosx+2xsinx sufficient, or should I factor out the x as well?

    I'd like more than one opinion guys.
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  2. #2
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    Quote Originally Posted by VonNemo19 View Post
    find the derivative

    x^2sinx

    It says simplify the result

    is x^2cosx+2xsinx sufficient, or should I factor out the x as well?

    I'd like more than one opinion guys.
    Questions that ask that (simplify the result) might as well also ask how long a piece of string is ....

    The fact is that different people will have a different idea of what simplify the result means ....

    However, since the basic answer can pretty much be written down by inspection in one line, I suspect the writer of the question wants you to factorise the answer. In which case, s/he should have just said to give your answer in factorised form.

    Personally I find the use of broad instructions such as "simplify your answer" and their ilk ridiculous in many cases. In your case, I would have thought that the intent of the question was to test a basic skill (use of product rule), that the question would be worth 1 mark and that your answer would be sufficient. In which case, the instruction to "simplify the result" is even more ridiculous since potentially a student could get zero even though s/he has succesfully applied the skill.

    Such instructions are especially potentially ridiculous in on-line tests. In my opinion, such a broad instruction usually makes the person who wrote the question look like a fool.

    Instructions I typically use include:

    ".... and completely factorise your answer."

    "Express your answer in exact surd form."

    "Find in exact form ...."

    "Find in the form a + b \ln (c) where a, b and c are whole numbers ...."

    "Find in the form y = mx + c the equation of the line ...."

    etc.

    In other words, I specifically prescibe the form I want the answer in.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Questions that ask that (simplify the result) might as well also ask how long a piece of string is ....

    The fact is that different people will have a different idea of what simplify the result means ....

    However, since the basic answer can pretty much be written down by inspection in one line, I suspect the writer of the question wants you to factorise the answer. In which case, s/he should have just said to give your answer in factorised form.

    Personally I find the use of broad instructions such as "simplify your answer" and their ilk ridiculous in many cases. In your case, I would have thought that the intent of the question was to test a basic skill (use of product rule), that the question would be worth 1 mark and that your answer would be sufficient. In which case, the instruction to "simplify the result" is even more ridiculous since potentially a student could get zero even though s/he has succesfully applied the skill.

    Such instructions are especially potentially ridiculous in on-line tests. In my opinion, such a broad instruction usually makes the person who wrote the question look like a fool.
    I've been thinking that the whole time. When my professor says "simplfy the result", contextually, this can mean a number of things. Also, he himself has shown many different examples of what "simplify" means, which makes this statement all the more confounding. I believe, however, by my own personal intuition, that leaving this result as it is, because there is nothing that will come of the answer. If I was going to try and find where the function had any critical points, factoring would then be appropriate. Am I right?

    p.s. I attend community college. My professor is by no means ivy elite.
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  4. #4
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    Quote Originally Posted by VonNemo19 View Post
    I've been thinking that the whole time. When my professor says "simplfy the result", contextually, this can mean a number of things. Also, he himself has shown many different examples of what "simplify" means, which makes this statement all the more confounding. I believe, however, by my own personal intuition, that leaving this result as it is, because there is nothing that will come of the answer.

    If I was going to try and find where the function had any critical points, factoring would then be appropriate. Am I right? Mr F says: Yes.

    p.s. I attend community college. My professor is by no means ivy elite.
    Another problem with needless simplifying of a correct answer is that if you make a careless error during that unnecessary process you will lose the answer mark because your final answer is the one that you live or die by ....
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  5. #5
    No one in Particular VonNemo19's Avatar
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    And, yet again, my sentiments exactly.
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