(\partial)/(\partial x)(4xcos(5xy))

解

\frac{\partial}{\partial x} (4 x cos (5 x y))

4 (cos (5 x y) - 5 x y sin (5 x y))

解答ステップ

\frac{\partial}{\partial x} (4 x cos (5 x y))

y

を定数として扱う

定数を除去:

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

= 4 \frac{\partial}{\partial x} (x cos (5 x y))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (5 x y)

= 4 (\frac{\partial}{\partial x} (x) cos (5 x y) + \frac{\partial}{\partial x} (cos (5 x y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (cos (5 x y)) = - sin (5 x y) \cdot 5 y

= 4 (1 \cdot cos (5 x y) + (- sin (5 x y) \cdot 5 y) x)

簡素化

= 4 (cos (5 x y) - 5 x y sin (5 x y))