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

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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