derivative of ln(x+y^2)

解

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

\frac{1 + 2 y \frac{d y}{d x}}{x + y ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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