derivative of arctan(x/2+arctan(2/x))

解

\frac{d}{d x} (arctan (\frac{x}{2}) + arctan (\frac{2}{x}))

0

解答ステップ

\frac{d}{d x} (arctan (\frac{x}{2}) + arctan (\frac{2}{x}))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arctan (\frac{x}{2})) + \frac{d}{d x} (arctan (\frac{2}{x}))

\frac{d}{d x} (arctan (\frac{x}{2})) = \frac{2}{x ^{2} + 4}

\frac{d}{d x} (arctan (\frac{2}{x})) = - \frac{2}{4 + x ^{2}}

= \frac{2}{x ^{2} + 4} - \frac{2}{4 + x ^{2}}

簡素化

\frac{2}{x ^{2} + 4} - \frac{2}{4 + x ^{2}} : 0

= 0