Derivatives Of Log. Functions... HELP!!! Calculus II is a Bitch!
 

I cant figure out derivatives of Logarithmic functions. Here's an example from my notes.


Problem: Y=ln(x^4(sin^2(x))) Find first derivative.

Y= ln(x^4) + ln(sin^2(x)) dx

Y= ln(x^4) + ln(sin(x))^2 dx

Y=4ln(x) + 2ln(sinx) dx

I get here, then I get stuck.

Y'= ???

My notes show Y'= (4/x) + (2cos(x))/(sin(x) But I don't see how they got that.

I'm pretty sure you have to use chain rule to get this answer, but I don't know I'm just not getting it. :confused:

I've even tried some of the online calculus calculators and they come up with different answers then the one from my notes.

Thanks for any help.

My personal opinion. :) Become a psychologist... the math is easier!

Mark

I'm with Mark, i stopped at Calc 1 for a reason.

:gay: I made a thread here about hating Calc II last semester. I'll be taking it again next semester. :td:

Edit: and I don't remember how to derive log functions either

'(ln(x))=1/x

Which gives you 2(sin(x)/x)
now go to your law of cos and sin

lol well once upon a time i could help you but well i don't remember anymore, sorry, what is your major?

my text book had a log derivatives table with general rules and such... made it so easy that I couldn't possibly do it without my book.... which is at the office, so you are out of luck,

I should line you out with my roommate, he's a double major, ME and Math.
Took calc 3 and dif-e the same semster, said it was a breeze. He finally has a hard class in school, dif-e 2 is making him hate life.

Thank you. Turns out my text book has Rules too. I don't know why but I just didn't see them before. I've got this figured out now, I just needed the rules to follow.

I didn't know there was a diff. between x^n and a^x. Of course, there is, and there are diff. rules for each. That was the main thing I was overlooking.

My major is Mechanical Engineering. This is my second year and next semester I'll be taking Calculus III, Linear Algerbra, Physics II, and Statics.:ugh2: I'm not exactly looking forward to it. The physics comes easy, but this calculus gets me triped up pretty regularly.

Loki, I see that lnx dx = 1/x, but I didn't follow the rest of that. Anyway, I've a few rules to use and so far they're working.

When i was in calc my book had all of the rules on in the back 2 pages and on the back of the rear cover.

:bowdown:

Damn it again. Sure enough, there's 3 pages of formulas back their I could have been using since Cal I. I guess I just never thought to look there. :vash:

Oh well, at least I've got all the people on this forum to set me straight.:bigtu:

Seriously, without those 3 pages i would have failed. Xerox those pages and put them in your notebook, on your wall, your g/fs wall. Just so you know as many of them as possible.

Yeap. I have a copy in my notebook now. That should definately help.

Loki, how do you remember how to do that?

i hate that shit, I'm doin absolute maxima and minima in calc. I now, dy/dx and limits ftl :td:

:rofl: I though it was hard at the time too, but actually it's just the foundation for the hard stuff that comes later. You'll get really good and really fast at it.
Wait until when (if) you get to the multivariate stuff. Ugh.

i just can't wait :ugh2:
I've also got a lab that uses Maple 11 software with my TA Arnab, but i see it as miataturbo.net time :bigtu:

you'll need to know that calc when you start taking the heat transfer and control system stuff. it's pretty useful.

oh goodie, this is what I have to look foward too next year when im a mechanical enginneer in college! woo hoo..

Stop posting this, it makes not want to go to school

Isn't this what software is for?!?

forty two.

Think Calc is hard...just wait for thermo. Nothing better than a take home test with one problem that takes 40hrs to complete.

It's even better when your professor's English is about as clear as mud.

I will say it is all worth it in the end. A professional salaried job makes playing with cars and racing a little easier. Stick with it!

:dunno:

That just leaves me with mental images of good will hunting.

Mark

I grdauated in May, my last math course was calc three sophomore year :dunno: to be honest I have no idea. Calc was never that hard for me, the problem is you have teachers instead of teaching you the overall concept and then walking you through derivations for each case, they try to teach you "rules" for each type, ie chain rule or whatever. It really didn't click until i took a class after differential equations that I cant remember the name of.

But pat, get one of those calculators that does everything. I had a voyage 200, but while they wouldn't let me use it in test it allowed me to double check all my answers for hw

Dude thermo is easy, just remember to assume everything doesnt exist, wait for heat trasnfer then you cant its all taken into account. If i ever have to nondimensionalize a problem again ill shoot myself in the face.

Hey Ben- When you used the product rule in step 3, Isn't the derivative of a constant Zero?

:ughug: loki you my math hero :love:

I've been thinking about doing that. I've always used my TI-83 that was given to me used 8 years ago:nono: Perhaps a higher level Texas Instruments? I've never heard of a Voyage before.

Indeed :o

Thanks Ben, that helps. Then you can simplify 2(cos/sin)x to 2cotx. That's the final answer in my notes, so that must be how to get to it.

Thanks everybody for all the help. This is the best turbochaged miata/Calculus help Forum in the world!!!

Right.
FWIW, I got help w/ that. There's a math major (grad w/ honors) in the kitchen. :gay:

2 things about the voyage, full keyboard, and usb port to plug into a computer. TO download notes to it ;)

Well, that's two good reasons right there:bigtu: Do any higer level calculators actually show the steps involved to solving the problem? Perhaps that's asking too much, but if I'm buying it to help me learn, that would be the deciding factor come time to buy one.

well i used to do the steps for each problem and then check it with the calc. I couldnt recommend it enough

That's what solutions manuals are for. If you google questions from the book alot of times you can find an uploaded solutions manual. Even bittorrent might have it.

Problem: Y=ln(x^4(sin^2(x))) Find first derivative.

=(d/dx) ln(x^4(sin^2(x)))
=4lnx+ 2lnsin^2x
=(4/x)+2(1/sinx)cosx
=(4/x)+2cotx

^^that is your answer
I have the same book but I am in calc one, i hate differentiations

*EDIT* sorry i didnt realize you already had the answer

btw, ticalc.org

you can download programs that help find the answer... its a good reference, but we arent allowed calculators

I dont think anyone is, cept for calc three cause those we impossible by hand (time wise)

At first it was kind of surprising how many college students were on this board, but I guess it makes sense. I'm about to finish up Tech Calc I. It hasn't been too bad. Hopefully Calc II will be the same, and I will be done with all that.
-Michael-

dear lord guys...that made my head hurt. I'm a History-Secondary Ed. major...you guys will be rolling in the dough and I'll be teaching kids not much younger than me about the world...and be poor doing it.

Yes, but you'll have to opportunity to run away to mexico with a 13 year old. ;) Crazy ass women teachers... what is up with them? More importantly, where were they when I was growing up? This last one is gonna go down hard though, she's screwed.

As an educator, if you want to be well off when you retire, get a job at South Side High School in Rockville Centre, NY. I hear that the retirement package for that school district can set you up nicely in just about anywhere else in the country. (Cost of living in RVC is stupid high.)

Mark

I am married to a teacher. 70k a year for 9 months work isn't too bad. Not to mention the job security (after tenure). No marketplace competition, no stress over productivity. True you won't get rich, but after like 5 years you can be plenty comfy. Just take a walk around a school staff parking lot sometime. BMers, Volvos, and $40k SUV's are the norm.

Damn. No wonder GA has such shitty schools; teachers here get 30-40k/yr. Including my mother, who has a master's, and has been teaching pre-k since all the kids left the house.

yeah teachers in KY get around 30K i think the higher level they teach the more money though. Still 30-40K is not the end of the world.

heh, the graduate level heat transfer makes the undergrad version seem like child's play. that class destroyed me :crx:

Man, in NC I'll start at like 28k...its utter bullshit.

Yeah i took that too, the problem was my professor is getting his book published in heat transfer. Basically he has a new method to solve problem involving heat exchangers.

Just as an update calculus still sucks. Derivatives of inverse trig functions FTL.

I just had to do that at work. I was setting up a crossing course simulation (aircraft flying past a point). The radar's azimuth angle roughly follows an arcsin path and I needed to find the velocity curve to check against my filters.

So there is a chance I could actually use some of this one day? I'm slowly figuring this stuff out but man it's hard. I'm averaging 2-3 problems correct an hour. It just takes me forever to figure these out.

The important thing is to remember that it can be done not exactly how to do it. That's what Google is for.

A co-worker of mine teaches calc at a night class. He didn't remember it either.

Now i understand why you were one of the people writing your own MSII code and testing the new beta.

Not that it helps, but I got an A for the semester in Stats... still can't integrate a function to save my ass.

Mark

Stats 330 is probably the easiest class I have this semester. I'm retaking calc II next semester, and I decided to do a business minor (bumps my major's avg starting salary to 65k), so i'm taking econ and marketing too.

Not bad for a starting salary. My starting salary for going to grad school was $40k plus $27k in housing, food, and other allowances. Who says the government doesn't pay well? ;) Some of the grad students are making bank though compared to me. $63K + $30K Allowances (some are making more than that...) $93K to go to grad school is pretty freaking sweet, especially compared to my $67k

Mark

I frickin aced stats, blew through it w/o an issue. Deborah, a math major who is capable of all sorts of advanced calculus I can't understand, can't handle stats to save her life.

yeah well i have to relearn how to integrate roots for a test at 11:15 :vash:

Calculus 2 Final Exam Friday... Scored a D on my last test and the final is on the same material, so I gotta figure this stuff out.:td: I'm barely hanging on to a C average and I have to have a C or better or I'll be taking it next semester. Wooo.