(\partial)/(\partial x)(14x^3cos(7x^2y))

解

\frac{\partial}{\partial x} (14 x^{3} cos (7 x^{2} y))

14 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

解答ステップ

\frac{\partial}{\partial x} (14 x^{3} cos (7 x^{2} y))

y

を定数として扱う

定数を除去:

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

= 14 \frac{\partial}{\partial x} (x^{3} cos (7 x^{2} y))

積の法則を適用:

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

f = x^{3}, g = cos (7 x^{2} y)

= 14 (\frac{\partial}{\partial x} (x^{3}) cos (7 x^{2} y) + \frac{\partial}{\partial x} (cos (7 x^{2} y)) x^{3})

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

\frac{\partial}{\partial x} (cos (7 x^{2} y)) = - sin (7 x^{2} y) \cdot 14 y x

= 14 (3 x^{2} cos (7 x^{2} y) + (- sin (7 x^{2} y) \cdot 14 y x) x^{3})

簡素化

14 (3 x^{2} cos (7 x^{2} y) + (- sin (7 x^{2} y) \cdot 14 y x) x^{3}) : 14 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))

= 14 (3 x^{2} cos (7 x^{2} y) - 14 x^{4} y sin (7 x^{2} y))