(\partial)/(\partial x)(ln(3x^2+4y^2+2))

解

\frac{\partial}{\partial x} (ln (3 x^{2} + 4 y^{2} + 2))

\frac{6 x}{3 x ^{2} + 4 y ^{2} + 2}

解答ステップ

\frac{\partial}{\partial x} (ln (3 x^{2} + 4 y^{2} + 2))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{3 x ^{2} + 4 y ^{2} + 2} \frac{\partial}{\partial x} (3 x^{2} + 4 y^{2} + 2)

= \frac{1}{3 x ^{2} + 4 y ^{2} + 2} \frac{\partial}{\partial x} (3 x^{2} + 4 y^{2} + 2)

\frac{\partial}{\partial x} (3 x^{2} + 4 y^{2} + 2) = 6 x

= \frac{1}{3 x ^{2} + 4 y ^{2} + 2} \cdot 6 x

簡素化

\frac{1}{3 x ^{2} + 4 y ^{2} + 2} \cdot 6 x : \frac{6 x}{3 x ^{2} + 4 y ^{2} + 2}

= \frac{6 x}{3 x ^{2} + 4 y ^{2} + 2}