derivative f(z)=sqrt((z-1)/(z+1))

解答

导数

f (z) = \frac{z - 1}{z + 1}

\frac{1}{z - 1 ( z + 1 ) ^{\frac{3}{2}}}

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

= \frac{1}{z - 1 ( z + 1 ) ^{\frac{3}{2}}}

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