簡約-5e^{-3x}(-sin^2(x)+cos(x)(3-cos(x)))

解

簡約

- 5 e^{- 3 x} (- sin^{2} (x) + cos (x) (3 - cos (x)))

- \frac{5 ( cos ( x ) ( - cos ( x ) + 3 ) - sin ^{2} ( x ) )}{e ^{3 x}}

解答ステップ

- 5 e^{- 3 x} (- sin^{2} (x) + cos (x) (3 - cos (x)))

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= - 5 \cdot \frac{1}{e ^{3 x}} (cos (x) (- cos (x) + 3) - sin^{2} (x))

分数を乗じる:

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

= - \frac{1 \cdot 5 ( - sin ^{2} ( x ) + cos ( x ) ( 3 - cos ( x ) ) )}{e ^{3 x}}

数を乗じる:

1 \cdot 5 = 5

= - \frac{5 ( cos ( x ) ( - cos ( x ) + 3 ) - sin ^{2} ( x ) )}{e ^{3 x}}