(\partial)/(\partial x)(ln(x^8-y^6))

解

\frac{\partial}{\partial x} (ln (x^{8} - y^{6}))

\frac{8 x ^{7}}{x ^{8} - y ^{6}}

解答ステップ

\frac{\partial}{\partial x} (ln (x^{8} - y^{6}))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{x ^{8} - y ^{6}} \frac{\partial}{\partial x} (x^{8} - y^{6})

= \frac{1}{x ^{8} - y ^{6}} \frac{\partial}{\partial x} (x^{8} - y^{6})

\frac{\partial}{\partial x} (x^{8} - y^{6}) = 8 x^{7}

= \frac{1}{x ^{8} - y ^{6}} \cdot 8 x^{7}

簡素化

\frac{1}{x ^{8} - y ^{6}} \cdot 8 x^{7} : \frac{8 x ^{7}}{x ^{8} - y ^{6}}

= \frac{8 x ^{7}}{x ^{8} - y ^{6}}