derivative ((10-(2))/((x)))*((3+(1))/((x)))

解

導関数

(\frac{10 - ( 2 )}{( x )}) \cdot (\frac{3 + ( 1 )}{( x )})

- \frac{64}{x ^{3}}

解答ステップ

\frac{d}{d x} (\frac{10 - 2}{x} \cdot \frac{3 + 1}{x})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= (10 - 2) (3 + 1) \frac{d}{d x} (\frac{1}{x} \cdot \frac{1}{x})

積の法則を適用:

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

f = \frac{1}{x}, g = \frac{1}{x}

= (10 - 2) (3 + 1) (\frac{d}{d x} (\frac{1}{x}) \frac{1}{x} + \frac{d}{d x} (\frac{1}{x}) \frac{1}{x})

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= (10 - 2) (3 + 1) ((- \frac{1}{x ^{2}}) \frac{1}{x} + (- \frac{1}{x ^{2}}) \frac{1}{x})

簡素化

(10 - 2) (3 + 1) ((- \frac{1}{x ^{2}}) \frac{1}{x} + (- \frac{1}{x ^{2}}) \frac{1}{x}) : - \frac{64}{x ^{3}}

= - \frac{64}{x ^{3}}