1
$\begingroup$

This problem is not solved.

$$ \begin{align} f(x) &=\log\ \sqrt{\frac{1+\sqrt{2}x +x^2}{1-\sqrt{2}x +x^2}}+\tan^{-1}\left(\frac{\sqrt{2}x}{1-x^2}\right) \cr \frac{df}{dx}&=\mathord? \end{align} $$

  • 1
    For the log term, you'll want to use properties of logarithms to simply *before* you differentiate. There's also probably a clever way to use the arctangent addition formula found here: http://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Arctangent_addition_formula2012-10-21
  • 0
    $\frac12\log(1+\sqrt{2}x+x^2) + \frac12\log(1-\sqrt{2}x+x^2)$ is what you logarithm simplifies to. After that, use the chain rule.2012-10-21
  • 1
    There should be a minus sign there between the logs, Michael.2012-10-22

1 Answers 1