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

解

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

\frac{8 x}{4 x ^{2} + 7 y ^{2} + 4}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (4 x^{2} + 7 y^{2} + 4) = 8 x

= \frac{1}{4 x ^{2} + 7 y ^{2} + 4} \cdot 8 x

簡素化

\frac{1}{4 x ^{2} + 7 y ^{2} + 4} \cdot 8 x : \frac{8 x}{4 x ^{2} + 7 y ^{2} + 4}

= \frac{8 x}{4 x ^{2} + 7 y ^{2} + 4}