Question

differentiate log(1+x^2) with respect to tan^-1(x)

Answer 1

$\frac{d}{dx}(log((1+x^2))=\frac{2x}{1+x^2}$

$\frac{d}{dx}(arctgx)=\frac{1}{1+x^2}$

Answer:

$\frac{d(log((1+x^2))}{d(arctgx)}=\frac{2x}{1+x^2}\cdot(1+x^2)=2x$