# More Advanced Derivative Of natural Log

• Feb 17th 2010, 03:22 PM
x5pyd3rx
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
• Feb 17th 2010, 03:28 PM
skeeter
Quote:

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

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

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

$\displaystyle \frac{dy}{dx} = \frac{x}{x^2-1} - \frac{x}{x^2+1}$
• Feb 17th 2010, 03:39 PM
x5pyd3rx
Shouldent the x's have coifecents of 2's because the derivative of x^2 is 2x not x?
• Feb 17th 2010, 03:41 PM
x5pyd3rx
never mind i see what you did. I totally forgot about the 1/2

And sorry for double posting