derivative of (((0.06x^2+17x+340))/x)

解

\frac{d}{d x} (\frac{( ( 0.06 x ^{2} ) + 17 x + 340 )}{x})

\frac{0.06 x ^{2} - 340}{x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{( ( 0.06 x ^{2} ) + 17 x + 340 )}{x})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 0.06 x ^{2} + 17 x + 340 ) x - \frac{d x}{d x} ( 0.06 x ^{2} + 17 x + 340 )}{x ^{2}}

\frac{d}{d x} (0.06 x^{2} + 17 x + 340) = 0.12 x + 17

\frac{d x}{d x} = 1

= \frac{( 0.12 x + 17 ) x - 1 \cdot ( 0.06 x ^{2} + 17 x + 340 )}{x ^{2}}

簡素化

\frac{( 0.12 x + 17 ) x - 1 \cdot ( 0.06 x ^{2} + 17 x + 340 )}{x ^{2}} : \frac{0.06 x ^{2} - 340}{x ^{2}}

= \frac{0.06 x ^{2} - 340}{x ^{2}}