How do you differentiate ln((x+1)/(x-1)) ?

1 Answer
Mar 11, 2016

d/dxln((x+1)/(x-1))=1/(x+1)-1/(x-1)

Explanation:

To avoid needing to use the quotient rule , we will use the property of logarithms that
log(a/b) = log(a)-log(b)

After that, we will use the chain rule as well as the known derivative d/dxln(x) = 1/x

d/dxln((x+1)/(x-1)) = d/dx(ln(x+1)-ln(x-1))

=d/dxln(x+1)-d/dxln(x-1)

=1/(x+1)(d/dx(x+1))-1/(x-1)(d/dx(x-1))

=1/(x+1)(1)-1/(x-1)(1)

=1/(x+1)-1/(x-1)