derivative of 2x^2y^2

解

\frac{d}{d x} (2 x^{2} y^{2})

2 (2 x y^{2} + 2 y \frac{d y}{d x} x^{2})

解答ステップ

\frac{d}{d x} (2 x^{2} y^{2})

定数を除去:

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

= 2 \frac{d}{d x} (x^{2} y^{2})

積の法則を適用:

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

f = x^{2}, g = y^{2}

= 2 (\frac{d}{d x} (x^{2}) y^{2} + \frac{d}{d x} (y^{2}) x^{2})

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

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

= 2 (2 x y^{2} + 2 y \frac{d y}{d x} x^{2})