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.

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.

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. 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.

 

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.

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

 

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 ****, I'm doin absolute maxima and minima in calc. I now, dy/dx and limits ftl

 

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
I've also got a lab that uses Maple 11 software with my TA Arnab, but i see it as miataturbo.net time

 

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