(\partial)/(\partial y)(7ln(2x^5-3y))

解

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))

- \frac{21}{2 x ^{5} - 3 y}

解答ステップ

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))

x

を定数として扱う

定数を除去:

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

= 7 \frac{\partial}{\partial y} (ln (2 x^{5} - 3 y))

連鎖法則を適用:

\frac{1}{2 x ^{5} - 3 y} \frac{\partial}{\partial y} (2 x^{5} - 3 y)

= \frac{1}{2 x ^{5} - 3 y} \frac{\partial}{\partial y} (2 x^{5} - 3 y)

\frac{\partial}{\partial y} (2 x^{5} - 3 y) = - 3

= 7 \cdot \frac{1}{2 x ^{5} - 3 y} (- 3)

簡素化

7 \cdot \frac{1}{2 x ^{5} - 3 y} (- 3) : - \frac{21}{2 x ^{5} - 3 y}

= - \frac{21}{2 x ^{5} - 3 y}