derivative (b/(a+z^2))^4

解

導関数

(\frac{b}{a + z ^{2}})^{4}

- \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

解答ステップ

\frac{d}{d z} ((\frac{b}{a + z ^{2}})^{4})

連鎖法則を適用:

4 (\frac{b}{a + z ^{2}})^{3} \frac{d}{d z} (\frac{b}{a + z ^{2}})

= 4 (\frac{b}{a + z ^{2}})^{3} \frac{d}{d z} (\frac{b}{a + z ^{2}})

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

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

簡素化

4 (\frac{b}{a + z ^{2}})^{3} (- \frac{2 b z}{( a + z ^{2} ) ^{2}}) : - \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

= - \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}