(\partial)/(\partial x)(-ysin(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)))

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)