Question

f(x)= ln x(x^2+1)^2/ln(x^3+1)^1/2 differentiate this

Answer 1

first expand the terms:
so u'll get,
\[f(x) = /\frac{\ln(x ^{3}+2x ^{2}+x} {\ln \sqrt{x ^{3}+1}}\]

Answer 2

now use this rule:
(u/v)' = (u'v - v'u)/v^2
it'll be a little complicated...but u'll be fine if u do it step-by-step. and i'm here to help.

Answer 3

thankx :)

Answer 4

is it ok if u apply both product rule and the quotient rule to solve this ??

Answer 5

how do u want to apply the product rule?

Answer 6

product rule for lnx(x^2+1)^2 part and then apply quotient rule to the whole thing

Answer 7

u can do that...but it'll just complicate things. u can either expand the x(x^2 +1)^2 and then just apply quotient rule...or u can simplify things this way:
ln x(x^2 +1)^2
=lnx + ln(x^2+1)^2
=lnx + 2ln(x^2+1)
and now just distribute the denominator to both these terms and differentiate.

Answer 8

i see... thank you for the help (Y)

Answer 9

sure! happy to help! see if u're getting the right answer.

Answer 10

oh btw...my first expansion was wrong! i just saw that its x^2...not just x.
so the numerator should be:
ln(x^5 + 2x^3 +x)