## anonymous 4 years ago Use logarithmic differentiation to find the derivative of the function: (Wolfram|Alpha didn't work)

1. anonymous

2. TuringTest

what did you get after taking the natural log of both sides?

3. anonymous

Thats what I'm having trouble with

4. TuringTest

you don't need to repost the problem I can still see it remember all you log rules, in particular these$\log(\frac a b)=\log a-\log b$$\log(x^a)=a\log x$then you will differentiate implicitly, which will allow you to solve for y'. why don't you try it and see how far you get?

5. TuringTest

rewriting this as$y=(\frac{x^2+1}{x^2-1})^{1/6}$should make it more clear

6. anonymous

So (x^2+1)-(x^2-1) = 2?

7. TuringTest

not quite...$y=(\frac{x^2+1}{x^2-1})^{1/6}$$\ln y=\ln(\frac{x^2+1}{x^2-1})^{1/6}=\frac1 6\ln(\frac{x^2+1}{x^2-1})=\frac1 6[\ln(x^2+1)-\ln(x^2-1)]$now differentiate both sides implicitly.