derivative of 3xy^2

解

\frac{d}{d x} (3 x y^{2})

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

解答ステップ

\frac{d}{d x} (3 x y^{2})

定数を除去:

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

= 3 \frac{d}{d x} (x y^{2})

積の法則を適用:

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

f = x, g = y^{2}

= 3 (\frac{d x}{d x} y^{2} + \frac{d}{d x} (y^{2}) x)

\frac{d x}{d x} = 1

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

= 3 (1 \cdot y^{2} + 2 y \frac{d y}{d x} x)

簡素化

= 3 (y^{2} + 2 x y \frac{d y}{d x})