(\partial)/(\partial x)(3y^6sin(3x))

解

\frac{\partial}{\partial x} (3 y^{6} sin (3 x))

9 y^{6} cos (3 x)

解答ステップ

\frac{\partial}{\partial x} (3 y^{6} sin (3 x))

y

を定数として扱う

定数を除去:

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

= 3 y^{6} \frac{\partial}{\partial x} (sin (3 x))

連鎖法則を適用:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= 3 y^{6} cos (3 x) \cdot 3

簡素化

= 9 y^{6} cos (3 x)