Derivatives of Log: Find f'(x) for f(x) = log10(x/x-1)

[10min]

Homework Statement

Question is
f(x) = log10(x/x-1), find f `(x)

Homework Equations

so I used the formula
d/dx loga(u) = 1/uLNa . (d/dx U)

The Attempt at a Solution

(1/(x/x-1)*ln10)*1/(x-1)^2 I used quotent rule for d/dx U part.

editing

Final Answer I got is

1/x(x-1)ln10
or
1/x2-x ln10
Please help
thank you

 

[lurflurf]

it may be easier to use the log property
log(ab)=log(a)+log(b)
log(x/(x-1))=log(x)-log(x-1)
[log10(x/(x-1))]'=[log(x/(x-1))]'/log(10)
=[log(x)-log(x-1)]'/log(10)
=([log(x)]'-[log(x-1)]')/log(10)

 

[10min]

so many answer is not right

 

[lurflurf]

so many answer is not right

Just a sign error
Quotient rule is
(u/v)'=(u'v-uv')/v^2
so
(x/(x-1))'=(x'(x-1)-x(x-1)')/(x-1)^2
=(1(x-1)-x(1))/(x-1)^2
=-1/(x-1)^2
not
1/(x-1)
also watch your grouping symbols
1/x2-x ln10
is confusing
try
1/[(x^2-x)ln 10]
or

[1/(x^2-x)]/ln 10