Thread: 2nd and 3rd Derivatives!!!!!

Hi! This is my last question, I need the 2nd and 3rd derivatives of (lnx) / (8x). I have the first derivative as being (8-8lnx) / (64x^2) is that right?? I'm not sure!!! And I need the next 2 derivatives!!! THank you!!!

OK, your first one is right on.
For the next two, just take the derivative of the derivative, then take the derivative of that!
Remember,

Okay, for the second, I got (64x^2)(-8/x)-(8-8lnx)(128x) all over 4096x^4. Is that right?

Let's go back to the first derivative (I didn't see this the first time)
Remember to reduce! You can pull an 8 out of there to get .
Either way, your answer is technically right.
I want you to simplify it, then post back with that.
After that, you should go ahead and take another derivative.

Oh okay, so if you take out a 8, then you're left with 1-lnx over 8x^2? So then finding the derivative of that, I got (-8x)-(1-lnx)(16x) all over 64x^4. Is that right?

Yep, but you still need to simplify this second derivative. What can you factor out of the top and the bottom?

An 8? So I got (-x)-(1-lnx)(2x) all over 8x^4. No?

You're pretty close.
You can get an x out too, so you get down to (-3+2ln(x)) over 8x^3
With that, you can then take its derivative and get the third derivative

Shouldn't it be all over 3x^4? How did you get 8x^3?

I have to go to dinner now, but I will work on it!! THank you so much for helping me!!!!

Well, 8x^4 is 8x^3*x, so that's that.
Have fun with supper! Glad to help, and tell your friends!

Thanks!! I will tell my friends!!! I love this forum!!!! Buuuut my calc 2 ends tomorrow and I dont have to take another math class ever again. I will tell others though!!!!!! Thanks!!

What a shame.
Well, go forth, then, into the realm of the world that doesn't make you take more math.
Maybe I'll get there someday.

hahaha okayyy!!