1. ## simplifying a derivative

find the derivative:

$\displaystyle x^2sinx$

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

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

I'd like more than one opinion guys.

2. Originally Posted by VonNemo19
find the derivative

$\displaystyle x^2sinx$

It says simplify the result

is $\displaystyle x^2cosx+2xsinx$ 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:

"Find in exact form ...."

"Find in the form $\displaystyle a + b \ln (c)$ 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.

3. Originally Posted by mr fantastic
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.

4. Originally Posted by VonNemo19
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 ....

5. And, yet again, my sentiments exactly.