(\partial)/(\partial x)(4ysin(x^2y))

解

\frac{\partial}{\partial x} (4 y sin (x^{2} y))

8 y^{2} x cos (y x^{2})

解答ステップ

\frac{\partial}{\partial x} (4 y sin (x^{2} y))

y

を定数として扱う

定数を除去:

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

= 4 y \frac{\partial}{\partial x} (sin (x^{2} y))

連鎖法則を適用:

cos (x^{2} y) \frac{\partial}{\partial x} (x^{2} y)

= cos (x^{2} y) \frac{\partial}{\partial x} (x^{2} y)

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

= 4 y cos (x^{2} y) \cdot 2 y x

簡素化

4 y cos (x^{2} y) \cdot 2 y x : 8 y^{2} x cos (y x^{2})

= 8 y^{2} x cos (y x^{2})