展开-e^{5x}*5(x^2+3x)

解答

展开

- e^{5 x} \cdot 5 (x^{2} + 3 x)

- 5 e^{5 x} x^{2} - 15 e^{5 x} x

求解步骤

- e^{5 x} \cdot 5 (x^{2} + 3 x)

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

使用分配律:

a (b + c) = ab + a c

a = - e^{5 x} \cdot 5, b = x^{2}, c = 3 x

= - e^{5 x} \cdot 5 x^{2} + (- e^{5 x} \cdot 5) \cdot 3 x

使用加减运算法则

+ (- a) = - a

= - 5 e^{5 x} x^{2} - 5 \cdot 3 e^{5 x} x

数字相乘:

5 \cdot 3 = 15

= - 5 e^{5 x} x^{2} - 15 e^{5 x} x

e x p an d (\frac{- 48}{6} bi g)^{2} (6 - 48) 2

e x p an d (, - 8) (- 16)^{'}

e x p an d cos ((2 - n) π)

e x p an d \frac{2}{3} (10.5 - 13, 5)

e x p an d [[v + \frac{1}{( 3 v - 1 ) ^{3}}] d x]