derivative of ln(x^2+2-y)

解

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

\frac{2 x - \frac{d y}{d x}}{x ^{2} + 2 - y}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{2 x - \frac{d y}{d x}}{x ^{2} + 2 - y}