Derivatives Of Log. Functions... HELP!!! Calculus II is a Bitch!
#1
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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.![](https://www.miataturbo.net/images/smilies/confused.gif)
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.
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.
![](https://www.miataturbo.net/images/smilies/confused.gif)
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.
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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.
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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.
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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.
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Oh well, at least I've got all the people on this forum to set me straight.
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Wait until when (if) you get to the multivariate stuff. Ugh.