derivative h(x)=(2/x-3)(x^2+7)

解

導関数

h (x) = (\frac{2}{x} - 3) (x^{2} + 7)

- \frac{2 ( x ^{2} + 7 )}{x ^{2}} + 4 - 6 x

解答ステップ

\frac{d}{d x} ((\frac{2}{x} - 3) (x^{2} + 7))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{2}{x} - 3, g = x^{2} + 7

= \frac{d}{d x} (\frac{2}{x} - 3) (x^{2} + 7) + \frac{d}{d x} (x^{2} + 7) (\frac{2}{x} - 3)

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

\frac{d}{d x} (x^{2} + 7) = 2 x

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

簡素化

(- \frac{2}{x ^{2}}) (x^{2} + 7) + 2 x (\frac{2}{x} - 3) : - \frac{2 ( x ^{2} + 7 )}{x ^{2}} + 4 - 6 x

= - \frac{2 ( x ^{2} + 7 )}{x ^{2}} + 4 - 6 x