Thread: Derivative question Help

I got my recent test back and one of the questions was to find dy/dx of the following:
ln( )... Sorry i had trouble writing it out formaly but its ln of whats in the bracket.

I seemed to solved it but i just ended up with a HUGE long denominator and ended up getting 2 marks out of 5 soo i was wondering if someone would be kind enough to solve this with the steps soo i can see where i went wrong. There are soo many brackets im just lost trying to trace it back. Thanks would be appriciated

I'm assuming you mean to take the derivative of

correct? If so, you need to use the chain rule first, then quotient, etc. What steps do you get?

What I would do is write

Originally Posted by Ackbeet

I'm assuming you mean to take the derivative of

correct? If so, you need to use the chain rule first, then quotient, etc. What steps do you get?

Yes correct, im new with this site soo i dont no how to formaly write it and the site i was using to change it made my ln into log
umm i basically did ln(u) and then solved the inside (u), seperatly and then subed it back in ln so i did 1/(my answer of dx/dy of u).
Got a huge mess because of the quotient rule and chain rules.

Im actually surprised i never thought of writing it the way Fobos3 wrote it.. seems like a correct way and much easier

fobos3's method is certainly valid as well. Warning: sometimes fobos3's method winds up being just as much work, because in order to simplify your answer you have to re-combine things. In this case, though, it does appear his method would be easier. Take your pick.

Originally Posted by Ackbeet

fobos3's method is certainly valid as well. Warning: sometimes fobos3's method winds up being just as much work, because in order to simplify your answer you have to re-combine things. In this case, though, it does appear his method would be easier. Take your pick.

I just have one more quick question... suppose the terms inside are added together, you can no longer use fobos3's method correct? Only ln(xy)=lnx+lny.. so what happens if we had ln(x+y) can you split to to lnx+lny?
For example : ln(x^2+x+1).. soo you cant write lnx^2+lnx+ln1 right?

The logarithm turns multiplication into addition, not the reverse. So your hunch is correct: fobos3's method will not work if the argument of the logarithm is a bunch of terms added together. You'll have to use the chain rule.