Differentiate y= ln l 1+t-t^3 l

Question

anonymous · Answer

$$\frac{ 1-3x^2 }{ 1+x-x^3 }$$

tkhunny · Answer

It should be viewed as kind of remarkable that the Absolute Values just sort of disappear.  Really, a fascinating thing to think about.

anonymous · Answer

ok, I see. I have another question relating to this one.  If the absolute values just sort of disappear   diff ln|cos(ln(x))|= diff ln(cos(ln(x))  is this right?

tkhunny · Answer

Don't go getting all hog-wild.  That comment was for a single situation and a very specific reference.

As for your other question, absolutely not.  The Domain of the two expressions is entirely different.

anonymous · Answer

so, when dealing with absolute situation, we need to take domain into account?

tkhunny · Answer

Delete the part where it says "so, when dealing with absolute situation," and you will be exactly correct.  Never, EVER forget about the Domain.