derivative of (5x-3(4x-3/x))

解

\frac{d}{d x} ((5 x - 3) (4 x - \frac{3}{x}))

40 x - \frac{9}{x ^{2}} - 12

解答ステップ

\frac{d}{d x} ((5 x - 3) (4 x - \frac{3}{x}))

簡素化

(5 x - 3) (4 x - \frac{3}{x}) : 20 x^{2} - 15 - 12 x + \frac{9}{x}

= \frac{d}{d x} (20 x^{2} - 15 - 12 x + \frac{9}{x})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (20 x^{2}) - \frac{d}{d x} (15) - \frac{d}{d x} (12 x) + \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (20 x^{2}) = 40 x

\frac{d}{d x} (15) = 0

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= 40 x - 0 - 12 - \frac{9}{x ^{2}}

簡素化

= 40 x - \frac{9}{x ^{2}} - 12