Question

Find derivative: f(u) = arctan(u/(1+u)

Answer 1

F ` ( x ) = 
$\frac{1}{1+ \frac{u ^{2} }{(1+u) ^{2} } } * ( \frac{u}{1+u})`= \\ = \frac{1}{ \frac{(1+u) ^{2}+ u^{2} }{(1+u) ^{2} } } * \frac{(u)`(1+u)-(1+u)` u}{(1+u) ^{2} } = \\ = \frac{(1+u) ^{2} }{(1+u) ^{2}+u ^{2} } * \frac{1+u-u}{(1+u) ^{2} } = \\ = \frac{1}{1+2u+2u ^{2} }$