## anonymous 4 years ago Use logarithmic differentiation to find the derivative of the function:

1. anonymous

2. anonymous

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

3. anonymous

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

4. anonymous

then multiply by the original function and you are done

5. anonymous

Why multiply by the original?

6. anonymous

oh because you are taking the log as the first step

7. anonymous

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

8. anonymous

Ah, so it its:

9. anonymous

is it correct?