Find dr/dx if
r = (lnx)/((x^2)lnx^2) + ln(1/x)^3
r' = lnx(x^2 lnx^2)^-1 + 3ln(1/x)
r' = 1/x(x^2 lnx^2)^-1 - lnx(x^2 lnx^2)(2x/x^2) + 3x --> first term I used chain and product rules, but I'm not sure if I carried them out correctly.
then I tried to combine stuff...
r' = 1/(x(x^2lnx^2) - lnx(x^2 lnx^2)(2x/x^2) + 3 --> is this the correct answer? None of the examples I saw in class still had "ln" in the final answer so I wasn't sure if I messed something up... (a high probability scenario).