Derivatives Of Log. Functions... HELP!!! Calculus II is a Bitch!
#1
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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.
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.
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. 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.
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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.
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.