derivative e^{z/((z-3))}

解答

导数

e^{\frac{z}{( z - 3 )}}

- \frac{3 e ^{\frac{z}{z - 3}}}{( z - 3 ) ^{2}}

求解步骤

\frac{d}{d z} (e^{\frac{z}{z - 3}})

使用连锁律:

e^{\frac{z}{z - 3}} \frac{d}{d z} (\frac{z}{z - 3})

= e^{\frac{z}{z - 3}} \frac{d}{d z} (\frac{z}{z - 3})

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

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

化简

e^{\frac{z}{z - 3}} (- \frac{3}{( z - 3 ) ^{2}}) : - \frac{3 e ^{\frac{z}{z - 3}}}{( z - 3 ) ^{2}}

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

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