derivative f(z)=e^{z/((z-5))}

解答

导数

f (z) = e^{\frac{z}{( z - 5 )}}

- \frac{5 e ^{\frac{z}{z - 5}}}{( z - 5 ) ^{2}}

求解步骤

\frac{d}{d z} (e^{\frac{z}{z - 5}})

使用连锁律:

e^{\frac{z}{z - 5}} \frac{d}{d z} (\frac{z}{z - 5})

= e^{\frac{z}{z - 5}} \frac{d}{d z} (\frac{z}{z - 5})

\frac{d}{d z} (\frac{z}{z - 5}) = - \frac{5}{( z - 5 ) ^{2}}

= e^{\frac{z}{z - 5}} (- \frac{5}{( z - 5 ) ^{2}})

化简

e^{\frac{z}{z - 5}} (- \frac{5}{( z - 5 ) ^{2}}) : - \frac{5 e ^{\frac{z}{z - 5}}}{( z - 5 ) ^{2}}

= - \frac{5 e ^{\frac{z}{z - 5}}}{( z - 5 ) ^{2}}

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