(\partial)/(\partial x)(ln(5x^2+4y^2+7))

解

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 7))

\frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

解答ステップ

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 7))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{5 x ^{2} + 4 y ^{2} + 7} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7)

= \frac{1}{5 x ^{2} + 4 y ^{2} + 7} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7)

\frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7) = 10 x

= \frac{1}{5 x ^{2} + 4 y ^{2} + 7} \cdot 10 x

簡素化

\frac{1}{5 x ^{2} + 4 y ^{2} + 7} \cdot 10 x : \frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

= \frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}