(\partial)/(\partial b)((a^3b^4)/(c^2d^4))

解

\frac{\partial}{\partial b} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

\frac{4 a ^{3} b ^{3}}{c ^{2} d ^{4}}

解答ステップ

\frac{\partial}{\partial b} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

定数を除去:

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

= \frac{a ^{3}}{c ^{2} d ^{4}} \frac{\partial}{\partial b} (b^{4})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{a ^{3}}{c ^{2} d ^{4}} \cdot 4 b^{4 - 1}

簡素化

\frac{a ^{3}}{c ^{2} d ^{4}} \cdot 4 b^{4 - 1} : \frac{4 a ^{3} b ^{3}}{c ^{2} d ^{4}}

= \frac{4 a ^{3} b ^{3}}{c ^{2} d ^{4}}