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I recently discovered logarithmic differentiation (Which was not taught to me at college for some reason) in the "Engineering Mathematics" book by Stroud. It striked me that the example and solved exercises were not fully simplified (They simply get to $f'(x)/ f(x)$ and then they multiply all of it by $f(x)$). This leaves a fairly big and (IMO) ugly product, which would probably be wrong at any test I have done (e.g. 4th edition, page 397, frame 25 exercise 4, I'm not going to copy that here because with my latex skills it would take two hours).

In some exercises, after doing whatever you need to do, you are asked to simplify the result. In others you don't. It seems to me that in this last case the decision of simplifying or not, and even the choice of making students simplify the result or not, is arbitrary. Is there any kind of rule or agreement about when to simplify something and when not? I haven't found anything so far and I find this apparent randomness very annoying.

I am wondering why sometimes textbooks and teachers simplify everything for half a page using confusing techniques that can potentially add mistakes to the result and consider the answer incorrect or not completely solved if you don't and other times they simply leave a number and symbol blob on the paper and consider it correct and perfectly valid.

Edit: A perfect example of this is the third exercise from the bottom in this page

  • For your info, if $f$ is differentiable on the range of $\log x$, then by the chain rule, we have $[\log(f(x))]' = \frac{1}{f(x)}*f'(x)$. – ireallydonknow Dec 30 '13 at 19:53
  • I understand how it works, I just don't get why in this cases the answers are not simplified and why in other similar exercises the answers MUST be simplified. –  Dec 30 '13 at 19:57
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    It's just... formality for some I guess? Gets you into the habit of making your workings look 'nicer'. – ireallydonknow Dec 30 '13 at 19:58
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    The answer in the example you give is correct. Amusingly, in principle the procedure is not, when $\sin x$ is negative. – André Nicolas Dec 30 '13 at 20:07
  • @AndréNicolas Nicely seen, thanks for pointing that out! –  Dec 30 '13 at 20:38
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    @Achifaifa : in a typical logarithmic differentiation problem, $\frac{dy}{dx}$ is going to be complicated no matter how much you try to simplify it, so most people don't bother trying. And if you do try to simplify it, it makes it harder to verify if it's correct. In other types of problems, an answer can often be significantly simplified. – Stefan Smith Dec 30 '13 at 21:10

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