(\partial)/(\partial x)(y(-sin(xln(y)))ln(y))

解

\frac{\partial}{\partial x} (y (- sin (x ln (y))) ln (y))

- y cos (x ln (y)) ln^{2} (y)

解答ステップ

\frac{\partial}{\partial x} (y (- sin (x ln (y))) ln (y))

y

を定数として扱う

定数を除去:

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

= y ln (y) \frac{\partial}{\partial x} (- sin (x ln (y)))

定数を除去:

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

= y ln (y) (- \frac{\partial}{\partial x} (sin (x ln (y))))

連鎖法則を適用:

cos (x ln (y)) \frac{\partial}{\partial x} (x ln (y))

= cos (x ln (y)) \frac{\partial}{\partial x} (x ln (y))

\frac{\partial}{\partial x} (x ln (y)) = ln (y)

= y ln (y) (- cos (x ln (y)) ln (y))

簡素化

y ln (y) (- cos (x ln (y)) ln (y)) : - y cos (x ln (y)) ln^{2} (y)

= - y cos (x ln (y)) ln^{2} (y)