derivative (-xsin(x)-cos(x))/(6x^2)

解

導関数

\frac{- x sin ( x ) - cos ( x )}{6 x ^{2}}

- \frac{x ^{2} cos ( x ) + 2 ( - x sin ( x ) - cos ( x ) )}{6 x ^{3}}

解答ステップ

\frac{d}{d x} (\frac{- x sin ( x ) - cos ( x )}{6 x ^{2}})

定数を除去:

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

= \frac{1}{6} \frac{d}{d x} (\frac{- x sin ( x ) - cos ( x )}{x ^{2}})

商の法則を適用:

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

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( - x sin ( x ) - cos ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( - x sin ( x ) - cos ( x ) )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (- x sin (x) - cos (x)) = - x cos (x)

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

= \frac{1}{6} \cdot \frac{( - x cos ( x ) ) x ^{2} - 2 x ( - x sin ( x ) - cos ( x ) )}{( x ^{2} ) ^{2}}

簡素化

\frac{1}{6} \cdot \frac{( - x cos ( x ) ) x ^{2} - 2 x ( - x sin ( x ) - cos ( x ) )}{( x ^{2} ) ^{2}} : - \frac{x ^{2} cos ( x ) + 2 ( - x sin ( x ) - cos ( x ) )}{6 x ^{3}}

= - \frac{x ^{2} cos ( x ) + 2 ( - x sin ( x ) - cos ( x ) )}{6 x ^{3}}