derivative of sqrt(2xy)^3

解

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

32 x (y + x \frac{d y}{d x}) y

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

3 (2 x y)^{2} \frac{y + x \frac{d y}{d x}}{2 x y} : 32 x (y + x \frac{d y}{d x}) y

= 32 x (y + x \frac{d y}{d x}) y