# Thread: More Advanced Derivative Of natural Log

1. ## More Advanced Derivative Of natural Log

This one has me stumped

$\displaystyle \ln (\sqrt{(\frac{1-x^2}{x^2+1}})$

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$\displaystyle \frac{1}{2} \ln \frac{1-x^2}{x^2 +1}$

This is where im stuck I belive that im right up to this part im not sure if i should do the quotient rule or the log propertie and turn it into a subtraciton problem. I tried turning it into subtraction but i got crazy numbers

2. Originally Posted by x5pyd3rx
This one has me stumped

$\displaystyle \ln (\sqrt{(\frac{1-x^2}{x^2+1}})$

| |
v

$\displaystyle \frac{1}{2} \ln \frac{1-x^2}{x^2 +1}$

This is where im stuck I belive that im right up to this part im not sure if i should do the quotient rule or the log propertie and turn it into a subtraciton problem. I tried turning it into subtraction but i got crazy numbers
$\displaystyle y = \ln {\sqrt{\frac{1-x^2}{x^2+1}}}$

$\displaystyle y = \frac{1}{2} \ln(1-x^2) - \frac{1}{2} \ln(x^2+1)$

$\displaystyle \frac{dy}{dx} = \frac{x}{x^2-1} - \frac{x}{x^2+1}$

3. Shouldent the x's have coifecents of 2's because the derivative of x^2 is 2x not x?

4. never mind i see what you did. I totally forgot about the 1/2

And sorry for double posting