derivative ((2+5z)/(5z))(15-2z)

解

導関数

(\frac{2 + 5 z}{5 z}) (15 - 2 z)

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

解答ステップ

\frac{d}{d z} (\frac{2 + 5 z}{5 z} (15 - 2 z))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d z} (\frac{2 + 5 z}{z} (15 - 2 z))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{2 + 5 z}{z}, g = 15 - 2 z

= \frac{1}{5} (\frac{d}{d z} (\frac{2 + 5 z}{z}) (15 - 2 z) + \frac{d}{d z} (15 - 2 z) \frac{2 + 5 z}{z})

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

\frac{d}{d z} (15 - 2 z) = - 2

= \frac{1}{5} ((- \frac{2}{z ^{2}}) (15 - 2 z) + (- 2) \frac{2 + 5 z}{z})

簡素化

\frac{1}{5} ((- \frac{2}{z ^{2}}) (15 - 2 z) + (- 2) \frac{2 + 5 z}{z}) : - \frac{2 ( z ^{2} + 3 )}{z ^{2}}

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