(\partial)/(\partial y)(x^2z^2sin(4y))

解

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

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

解答ステップ

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

x, z

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

cos (4 y) \frac{\partial}{\partial y} (4 y)

= cos (4 y) \frac{\partial}{\partial y} (4 y)

\frac{\partial}{\partial y} (4 y) = 4

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