d/(d{y)}(({z}(y,x))((3{x}+5{y})^7))

解

\frac{d}{d y} ((z (y, x)) ((3 x + 5 y)^{7}))

z (y, x) \cdot 7 (3 x + 5 y)^{6} \cdot 5

解答ステップ

\frac{d}{d y} ((z (y, x)) ((3 x + 5 y)^{7}))

定数を除去:

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

= z (y, x) \frac{d}{d y} ((3 x + 5 y)^{7})

連鎖法則を適用:

7 (3 x + 5 y)^{6} \frac{d}{d y} (3 x + 5 y)

= 7 (3 x + 5 y)^{6} \frac{d}{d y} (3 x + 5 y)

\frac{d}{d y} (3 x + 5 y) = 5

= z (y, x) \cdot 7 (3 x + 5 y)^{6} \cdot 5