(\partial)/(\partial x)(ln(9+x^2+3y^2))

解

\frac{\partial}{\partial x} (ln (9 + x^{2} + 3 y^{2}))

\frac{2 x}{9 + x ^{2} + 3 y ^{2}}

解答ステップ

\frac{\partial}{\partial x} (ln (9 + x^{2} + 3 y^{2}))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{9 + x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + 3 y^{2})

= \frac{1}{9 + x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (9 + x^{2} + 3 y^{2}) = 2 x

= \frac{1}{9 + x ^{2} + 3 y ^{2}} \cdot 2 x

簡素化

\frac{1}{9 + x ^{2} + 3 y ^{2}} \cdot 2 x : \frac{2 x}{9 + x ^{2} + 3 y ^{2}}

= \frac{2 x}{9 + x ^{2} + 3 y ^{2}}