Answer to Question #204089 in Calculus for moe

Question

What is the derivative of $y = arctanx/ln2x$

Answer 1

Let us find the derivative of $y =\frac{ \arctan x}{\ln 2x}:$

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