Question

Use logarithmic differentiation to find the derivative of the function:

Answer 1

start with
\[\ln(y)=\frac{1}{6}(\ln(x^2+1)-\ln(x+1)-\ln(x-1))\] then take the derivative term by term

Answer 2

\[\frac{1}{6}\left (\frac{2x}{(x^2+1)}-\frac{1}{x+1}-\frac{1}{x-1}\right )\]

Answer 3

then multiply by the original function and you are done

Answer 4

Why multiply by the original?

Answer 5

oh because you are taking the log as the first step

Answer 6

\[\frac{d}{dx}\left[\ln(f(x))\right]=\frac{f'(x)}{f(x)}\iff f'(x)=f(x)\times \frac{d}{dx}\left[\ln(f(x))\right ]\]

Answer 7

Ah, so it its:

Answer 8

is it correct?