(\partial)/(\partial x)(ln(6x^2+7y^2+7))

解

\frac{\partial}{\partial x} (ln (6 x^{2} + 7 y^{2} + 7))

\frac{12 x}{6 x ^{2} + 7 y ^{2} + 7}

解答ステップ

\frac{\partial}{\partial x} (ln (6 x^{2} + 7 y^{2} + 7))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{6 x ^{2} + 7 y ^{2} + 7} \frac{\partial}{\partial x} (6 x^{2} + 7 y^{2} + 7)

= \frac{1}{6 x ^{2} + 7 y ^{2} + 7} \frac{\partial}{\partial x} (6 x^{2} + 7 y^{2} + 7)

\frac{\partial}{\partial x} (6 x^{2} + 7 y^{2} + 7) = 12 x

= \frac{1}{6 x ^{2} + 7 y ^{2} + 7} \cdot 12 x

簡素化

\frac{1}{6 x ^{2} + 7 y ^{2} + 7} \cdot 12 x : \frac{12 x}{6 x ^{2} + 7 y ^{2} + 7}

= \frac{12 x}{6 x ^{2} + 7 y ^{2} + 7}