derivative f(z)=sqrt((z-4)/(z+4))

解

導関数

f (z) = \frac{z - 4}{z + 4}

\frac{4}{z - 4 ( z + 4 ) ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d z} (\frac{z - 4}{z + 4})

連鎖法則を適用:

\frac{1}{2 \frac{z - 4}{z + 4}} \frac{d}{d z} (\frac{z - 4}{z + 4})

= \frac{1}{2 \frac{z - 4}{z + 4}} \frac{d}{d z} (\frac{z - 4}{z + 4})

\frac{d}{d z} (\frac{z - 4}{z + 4}) = \frac{8}{( z + 4 ) ^{2}}

= \frac{1}{2 \frac{z - 4}{z + 4}} \cdot \frac{8}{( z + 4 ) ^{2}}

簡素化

\frac{1}{2 \frac{z - 4}{z + 4}} \cdot \frac{8}{( z + 4 ) ^{2}} : \frac{4}{z - 4 ( z + 4 ) ^{\frac{3}{2}}}

= \frac{4}{z - 4 ( z + 4 ) ^{\frac{3}{2}}}