(\partial)/(\partial x)(3cos(3x+4y))

解

\frac{\partial}{\partial x} (3 cos (3 x + 4 y))

- 9 sin (3 x + 4 y)

解答ステップ

\frac{\partial}{\partial x} (3 cos (3 x + 4 y))

y

を定数として扱う

定数を除去:

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

= 3 \frac{\partial}{\partial x} (cos (3 x + 4 y))

連鎖法則を適用:

- sin (3 x + 4 y) \frac{\partial}{\partial x} (3 x + 4 y)

= - sin (3 x + 4 y) \frac{\partial}{\partial x} (3 x + 4 y)

\frac{\partial}{\partial x} (3 x + 4 y) = 3

= 3 (- sin (3 x + 4 y) \cdot 3)

簡素化

= - 9 sin (3 x + 4 y)