(x/(4x-3ln(x)))^'

解

(\frac{x}{4 x - 3 ln ( x )})^{^{'}}

\frac{- 3 ln ( x ) + 3}{( 4 x - 3 ln ( x ) ) ^{2}}

解答ステップ

(\frac{x}{4 x - 3 ln ( x )})^{'}

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{x ^{^{'}} ( 4 x - 3 ln ( x ) ) - ( 4 x - 3 ln ( x ) ) ^{^{'}} x}{( 4 x - 3 ln ( x ) ) ^{2}}

x^{'} = 1

(4 x - 3 ln (x))^{'} = 4 - \frac{3}{x}

= \frac{1 \cdot ( 4 x - 3 ln ( x ) ) - ( 4 - \frac{3}{x} ) x}{( 4 x - 3 ln ( x ) ) ^{2}}

簡素化

\frac{1 \cdot ( 4 x - 3 ln ( x ) ) - ( 4 - \frac{3}{x} ) x}{( 4 x - 3 ln ( x ) ) ^{2}} : \frac{- 3 ln ( x ) + 3}{( 4 x - 3 ln ( x ) ) ^{2}}

= \frac{- 3 ln ( x ) + 3}{( 4 x - 3 ln ( x ) ) ^{2}}