I'm having a little trouble differentiating these two functions, if anyone could help I would greatlyyy appreciate it.
g(x) = ln (x * sqrt(x^(2)-1))
and
f(u) = ln u / (1+ln(2u))
Whatever I do that makes sense to me, I end up with (1/x) + ((x) / (x^(2) - 1)) for g(x) and for the second, I used the quotient rule and can't end up with anything similar to the answers for either. Thank you very much in advance!
Yup!
Differentiate, either by writing it as [LaTeX ERROR: Convert failed] and using the chain rule, or using the quotient rule (as laid out earlier in the thread), and we will just work out how what we get is equivalent to the book's answer... don't worry about the simplification for now.[LaTeX ERROR: Convert failed]
Ah, thank you very much! I worked it all out now and I believe I have it correct...I didn't know ln(2u) - ln(u) could just be ln(2) for f(u). Although I'm not sure where the 2u in the denominator goes...but I guess I'll figure it out haha. For f(u) I got the same as in the book, but with a 2u in the denominator as well.
Isn't the book's answer [LaTeX ERROR: Convert failed] If so, then you were obviously meant to have the [LaTeX ERROR: Convert failed] in the denominator. If it's [LaTeX ERROR: Convert failed] , then it's because [LaTeX ERROR: Convert failed] . It isn't important to get the answer in the exact form as in the book anyway... it's alright as far as it's correct and sufficiently simplified.