(\partial)/(\partial x)(tan(ln(x*y)))

解

\frac{\partial}{\partial x} (tan (ln (x \cdot y)))

\frac{sec ^{2} ( ln ( x y ) )}{x}

解答ステップ

\frac{\partial}{\partial x} (tan (ln (x y)))

y

を定数として扱う

連鎖法則を適用:

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

= sec^{2} (ln (x y)) \frac{\partial}{\partial x} (ln (x y))

\frac{\partial}{\partial x} (ln (x y)) = \frac{1}{x}

= sec^{2} (ln (x y)) \frac{1}{x}

簡素化

sec^{2} (ln (x y)) \frac{1}{x} : \frac{sec ^{2} ( ln ( x y ) )}{x}

= \frac{sec ^{2} ( ln ( x y ) )}{x}