展開する (5x^6(-6xtan(6x)+7))/(7sec(6x))

解

展開する

\frac{5 x ^{6} ( - 6 x tan ( 6 x ) + 7 )}{7 sec ( 6 x )}

- \frac{30 x ^{7} tan ( 6 x )}{7 sec ( 6 x )} + \frac{5 x ^{6}}{sec ( 6 x )}

解答ステップ

\frac{5 x ^{6} ( - 6 x tan ( 6 x ) + 7 )}{7 sec ( 6 x )}

拡張

5 x^{6} (- 6 x tan (6 x) + 7) : - 30 x^{7} tan (6 x) + 35 x^{6}

= \frac{- 30 x ^{7} tan ( 6 x ) + 35 x ^{6}}{7 sec ( 6 x )}

分数の規則を適用する:

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

\frac{- 30 x ^{7} tan ( 6 x ) + 35 x ^{6}}{7 sec ( 6 x )} = - \frac{30 x ^{7} tan ( 6 x )}{7 sec ( 6 x )} + \frac{35 x ^{6}}{7 sec ( 6 x )}

= - \frac{30 x ^{7} tan ( 6 x )}{7 sec ( 6 x )} + \frac{35 x ^{6}}{7 sec ( 6 x )}

数を割る:

\frac{35}{7} = 5

= - \frac{30 x ^{7} tan ( 6 x )}{7 sec ( 6 x )} + \frac{5 x ^{6}}{sec ( 6 x )}