Math CONTINUATION OF QUESTION FROM bobpursley
posted by KIKSY on .
Thank you for answering the question before bobpursley,
I understand how you did the deriv of inside, outside, but how do I now do the second derivative since you have the extra 18x^2 in the numerator??
Thank you very much! (I suppose I have to brush up on my derivatives)
Posted by KIKSY on Thursday, March 10, 2011 at 8:52pm.
What is the first and second derivative of 3/(1+2(x^3)) ?
im tempted to do the quotient rule, but this looks weird to me...any advice would be greatly appreciated!!
Math  bobpursley, Thursday, March 10, 2011 at 8:55pm
let u=(1+2x^3)
then f= 3u^1
f'= 3 *u^2 *u'
but u'= 6x^2
so f'= 3*6x^2 /(1+2x^3)^2

I don't think bobpursley is on line, so permit me to continue ...
from Bob, y' = 18x^2(1+2x^3)2
so using the product rule and chain rule combination
y'' = 18x^2)(2)(1+2x^3)^3(6x^2) + (1+2x^2)^2(36x)
= 216x^4(1+2x^3)^3  36x(1+2x^3)^2
= 36x(1+2x^3)^3 [ 6x^3  (1+2x^3)]
= 36x(1+2x^3)^3 (4x^31)
or
= 36x(4x^31)/(1+2x^3)^3