簡約 (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x)

解

簡約

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

- \frac{y ^{2}}{2 x ^{2}} + \frac{8 y}{7 x} - \frac{3}{7} (ln (y) - ln (x))

解答ステップ

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{y}{x}) = ln (y) - ln (x)

= \frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} (ln (y) - ln (x))

\frac{- ( \frac{y}{x} ) ^{2}}{2} = - \frac{y ^{2}}{2 x ^{2}}

= - \frac{y ^{2}}{2 x ^{2}} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} (ln (y) - ln (x))

乗じる

\frac{8}{7} \cdot \frac{y}{x} : \frac{8 y}{7 x}

= - \frac{y ^{2}}{2 x ^{2}} + \frac{8 y}{7 x} - \frac{3}{7} (ln (y) - ln (x))