derivative of sqrt(2x+3y)

解

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

\frac{2 + 3 \frac{d y}{d x}}{2 2 x + 3 y}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 2 x + 3 y} (2 + 3 \frac{d y}{d x}) : \frac{2 + 3 \frac{d y}{d x}}{2 2 x + 3 y}

= \frac{2 + 3 \frac{d y}{d x}}{2 2 x + 3 y}