derivative of 4xy^3

解

\frac{d}{d x} (4 x y^{3})

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

解答ステップ

\frac{d}{d x} (4 x y^{3})

定数を除去:

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

= 4 \frac{d}{d x} (x y^{3})

積の法則を適用:

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

f = x, g = y^{3}

= 4 (\frac{d x}{d x} y^{3} + \frac{d}{d x} (y^{3}) x)

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

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

= 4 (1 \cdot y^{3} + 3 y^{2} \frac{d y}{d x} x)

簡素化

= 4 (y^{3} + 3 x y^{2} \frac{d y}{d x})