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

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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