(\partial)/(\partial x)(-sin(x^2y)x^2)

解

\frac{\partial}{\partial x} (- sin (x^{2} y) x^{2})

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

解答ステップ

\frac{\partial}{\partial x} (- sin (x^{2} y) x^{2})

y

を定数として扱う

定数を除去:

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

= - \frac{\partial}{\partial x} (sin (x^{2} y) x^{2})

積の法則を適用:

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

f = sin (x^{2} y), g = x^{2}

= - (\frac{\partial}{\partial x} (sin (x^{2} y)) x^{2} + \frac{\partial}{\partial x} (x^{2}) sin (x^{2} y))

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

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

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

簡素化

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

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