展開する ((1-x^2)sin(x)-xcos(2x))/(tan(x^3))

解

展開する

\frac{( 1 - x ^{2} ) sin ( x ) - x cos ( 2 x )}{tan ( x ^{3} )}

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

解答ステップ

\frac{( 1 - x ^{2} ) sin ( x ) - x cos ( 2 x )}{tan ( x ^{3} )}

拡張

(1 - x^{2}) sin (x) - x cos (2 x) : sin (x) - x^{2} sin (x) - x cos (2 x)

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

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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