Hi, this is kinda urgent so please respond quickly if you can.
My "root" function (dunno if it's called that in English, I'm from Austria) is:
f(x) = 2x • lnx
My first "derivative" (?) is:
f'(x) = 2 • lnx + 2
Now my question is what the second derivative would be. I don't know how to apply the rules here since I have a multiplication and an addittion there.
Is this correct:
f''(x) = 2/x + lnx
Hi, thanks for your reply. I don't understand why it is 2/x. The rules for differentiating are:
f(x) = u • v ........ f'(x) = u' • v + u • v'
f(x) = u + v ........ f'(x) = u' + v'
My comprehension problem is: how are these two rules combined when you have something like:
f(x) = u • v + s
(Like I have^^)
I would think:
f'(x) = u' • v + u • v' + s'
That would give me:
f'(x) = lnx + 2 • (1/x) + 0 = 2/x + lnx
What am I missing??? (I have the feeling it's something to do with constants vs variables but I can't figure it out.)
Edit: Actually, I think I know how you did it. In my formula reference there is a rule like this:
y = k • f(x) ........ y' = k • f'(x) CONSTANT FACTOR IS KEPT
That works when you consider the first "2" (from f(x) = 2 • lnx + 2) to be "k" and the rest ("lnx + 2") f(x). But there is another formula right above that one in my reference book that goes like this:
y = f(x) + k ........ y' = f'(x) CONSTANT SUMMAND IS OMITTED
And "2 • lnx" could be considered as "f(x)" and the last "2" as the summand ("k"), then you would get what I got. So is this a matter of which rule takes precedence? If so, when do I use the rule, with which I would get my (wrong) result in my current function here?