derivative f(x)=(x^2-5x+2)(x-2/x)

解

導関数

f (x) = (x^{2} - 5 x + 2) (x - \frac{2}{x})

3 x^{2} - 10 x + \frac{4}{x ^{2}}

解答ステップ

\frac{d}{d x} ((x^{2} - 5 x + 2) (x - \frac{2}{x}))

簡素化

(x^{2} - 5 x + 2) (x - \frac{2}{x}) : x^{3} - 5 x^{2} - \frac{4}{x} + 10

= \frac{d}{d x} (x^{3} - 5 x^{2} - \frac{4}{x} + 10)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (5 x^{2}) - \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (10)

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{d}{d x} (10) = 0

= 3 x^{2} - 10 x - (- \frac{4}{x ^{2}}) + 0

簡素化

= 3 x^{2} - 10 x + \frac{4}{x ^{2}}