derivative of ln(7x^2+9y^2)

解

\frac{d}{d x} (ln (7 x^{2} + 9 y^{2}))

\frac{14 x + 18 y \frac{d y}{d x}}{7 x ^{2} + 9 y ^{2}}

解答ステップ

\frac{d}{d x} (ln (7 x^{2} + 9 y^{2}))

連鎖法則を適用:

\frac{1}{7 x ^{2} + 9 y ^{2}} \frac{d}{d x} (7 x^{2} + 9 y^{2})

= \frac{1}{7 x ^{2} + 9 y ^{2}} \frac{d}{d x} (7 x^{2} + 9 y^{2})

\frac{d}{d x} (7 x^{2} + 9 y^{2}) = 14 x + 18 y \frac{d y}{d x}

= \frac{1}{7 x ^{2} + 9 y ^{2}} (14 x + 18 y \frac{d y}{d x})

簡素化

\frac{1}{7 x ^{2} + 9 y ^{2}} (14 x + 18 y \frac{d y}{d x}) : \frac{14 x + 18 y \frac{d y}{d x}}{7 x ^{2} + 9 y ^{2}}

= \frac{14 x + 18 y \frac{d y}{d x}}{7 x ^{2} + 9 y ^{2}}