(\partial)/(\partial x)(5sin(2(5x+6y)))

解

\frac{\partial}{\partial x} (5 sin (2 (5 x + 6 y)))

50 cos (2 (5 x + 6 y))

解答ステップ

\frac{\partial}{\partial x} (5 sin (2 (5 x + 6 y)))

y

を定数として扱う

定数を除去:

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

= 5 \frac{\partial}{\partial x} (sin (2 (5 x + 6 y)))

連鎖法則を適用:

cos (2 (5 x + 6 y)) \frac{\partial}{\partial x} (2 (5 x + 6 y))

= cos (2 (5 x + 6 y)) \frac{\partial}{\partial x} (2 (5 x + 6 y))

\frac{\partial}{\partial x} (2 (5 x + 6 y)) = 10

= 5 cos (2 (5 x + 6 y)) \cdot 10

簡素化

= 50 cos (2 (5 x + 6 y))