簡約 (3)(e^{0.6x})+9ln(2x^5)+(8)cos(2x)-9

解

簡約

(3) (e^{0.6 x}) + 9 ln (2 x^{5}) + (8) cos (2 x) - 9

3 e^{0.6 x} + 9 ln (2) + 45 ln (x) + 8 cos (2 x) - 9

解答ステップ

(3) (e^{0.6 x}) + 9 ln (2 x^{5}) + (8) cos (2 x) - 9

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

9 ln (2 x^{5}) = 9 ln (2) + 9 ln (x^{5})

= (3) (e^{0.6 x}) + 9 ln (2) + 9 ln (x^{5}) + (8) cos (2 x) - 9

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{5}) = 5 ln (x)

= 3 e^{0.6 x} + 9 ln (2) + 9 \cdot 5 ln (x) + 8 cos (2 x) - 9

数を乗じる:

9 \cdot 5 = 45

= 3 e^{0.6 x} + 9 ln (2) + 45 ln (x) + 8 cos (2 x) - 9