derivative 1/(2sqrt(t+4i))+2j

解

導関数

\frac{1}{2 t + 4 i} + 2 j

- \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d t} (\frac{1}{2 t + 4 i} + 2 j)

和/差の法則を適用:

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

= \frac{d}{d t} (\frac{1}{2 t + 4 i}) + \frac{d}{d t} (2 j)

\frac{d}{d t} (\frac{1}{2 t + 4 i}) = - \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}}

\frac{d}{d t} (2 j) = 0

= - \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}} + 0

簡素化

= - \frac{1}{4 ( t + 4 i ) ^{\frac{3}{2}}}