(\partial)/(\partial x)(ln(x^4-y^4))

解

\frac{\partial}{\partial x} (ln (x^{4} - y^{4}))

\frac{4 x ^{3}}{x ^{4} - y ^{4}}

解答ステップ

\frac{\partial}{\partial x} (ln (x^{4} - y^{4}))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{x ^{4} - y ^{4}} \frac{\partial}{\partial x} (x^{4} - y^{4})

= \frac{1}{x ^{4} - y ^{4}} \frac{\partial}{\partial x} (x^{4} - y^{4})

\frac{\partial}{\partial x} (x^{4} - y^{4}) = 4 x^{3}

= \frac{1}{x ^{4} - y ^{4}} \cdot 4 x^{3}

簡素化

\frac{1}{x ^{4} - y ^{4}} \cdot 4 x^{3} : \frac{4 x ^{3}}{x ^{4} - y ^{4}}

= \frac{4 x ^{3}}{x ^{4} - y ^{4}}