Question

differentiate f(x) = (lnx)/(1-x)

Answer 1

use the quotient rule

Answer 2

d(u/v)/dx = v*du/dx - u * dv/dx
-------------------
v^2

Answer 3

i used product rule and i got (x-x^2+lnx)/(1-x^2) i just want to check

Answer 4

i let u=lnx v=(1-x)^-1 du/dx=1/x and dv/dx=1/(1-x)^2

Answer 5

oh ok that's lnx (1-x)^-1

derivative is lnx * -(1-x)-2 *-1 + (1-x)^-1 * (1/x)

Answer 6

ya,so im kinda unsure coz im suppose to find f'(1). but i get 0/0

Answer 7

\[f'(x) =\frac{ x-x^{2}+lnx }{ (1-x)^{2} }\]

Answer 8

hmm i'll try simplifying...

Answer 9

I get

x lnx - x + 1
-----------
x(1 - x)^2

Answer 10

hm,, it will still get 0/0 so the answer for f'(1) =0?

Answer 11

yes still 0/0 - no 0/0 in indeterminate

Answer 12

i'll just recheck my working...

Answer 13

i see, okay thanks!

Answer 14

yes I still get same value for f'(x) using the quotient rule

so f'(1) is indeterminate

Answer 15

okay thank you very much!(:

Answer 16

yw as it happened it was easier to use the quotient rule in this case