(\partial)/(\partial x)(ln(8x^2+7y^2+9))

解

\frac{\partial}{\partial x} (ln (8 x^{2} + 7 y^{2} + 9))

\frac{16 x}{8 x ^{2} + 7 y ^{2} + 9}

解答ステップ

\frac{\partial}{\partial x} (ln (8 x^{2} + 7 y^{2} + 9))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{8 x ^{2} + 7 y ^{2} + 9} \frac{\partial}{\partial x} (8 x^{2} + 7 y^{2} + 9)

= \frac{1}{8 x ^{2} + 7 y ^{2} + 9} \frac{\partial}{\partial x} (8 x^{2} + 7 y^{2} + 9)

\frac{\partial}{\partial x} (8 x^{2} + 7 y^{2} + 9) = 16 x

= \frac{1}{8 x ^{2} + 7 y ^{2} + 9} \cdot 16 x

簡素化

\frac{1}{8 x ^{2} + 7 y ^{2} + 9} \cdot 16 x : \frac{16 x}{8 x ^{2} + 7 y ^{2} + 9}

= \frac{16 x}{8 x ^{2} + 7 y ^{2} + 9}