(\partial)/(\partial x)(20sin(4x)cos(2y))

解

\frac{\partial}{\partial x} (20 sin (4 x) cos (2 y))

80 cos (4 x) cos (2 y)

解答ステップ

\frac{\partial}{\partial x} (20 sin (4 x) cos (2 y))

y

を定数として扱う

定数を除去:

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

= 20 cos (2 y) \frac{\partial}{\partial x} (sin (4 x))

連鎖法則を適用:

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

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

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

= 20 cos (2 y) cos (4 x) \cdot 4

簡素化

= 80 cos (4 x) cos (2 y)