derivative 5arccot(t)+5arccot(1/t)

解

導関数

5 arccot (t) + 5 arccot (\frac{1}{t})

0

解答ステップ

\frac{d}{d t} (5 arccot (t) + 5 arccot (\frac{1}{t}))

和/差の法則を適用:

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

= \frac{d}{d t} (5 arccot (t)) + \frac{d}{d t} (5 arccot (\frac{1}{t}))

\frac{d}{d t} (5 arccot (t)) = - \frac{5}{t ^{2} + 1}

\frac{d}{d t} (5 arccot (\frac{1}{t})) = \frac{5}{1 + t ^{2}}

= - \frac{5}{t ^{2} + 1} + \frac{5}{1 + t ^{2}}

簡素化

- \frac{5}{t ^{2} + 1} + \frac{5}{1 + t ^{2}} : 0

= 0