展开 x(e^x+xe^x)

解答

展开

x (e^{x} + x e^{x})

e^{x} x + e^{x} x^{2}

求解步骤

x (e^{x} + x e^{x})

= x (e^{x} + e^{x} x)

使用分配律:

a (b + c) = ab + a c

a = x, b = e^{x}, c = x e^{x}

= x e^{x} + xx e^{x}

= e^{x} x + e^{x} xx

e^{x} xx = e^{x} x^{2}

= e^{x} x + e^{x} x^{2}

e x p an d \frac{6}{( x - 6 ) ( x + 1 )}

e x p an d (48 3^{22} + 7 \cdot 3^{21}) \cdot 57 z

e x p an d (x^{2} + y^{2} + 1) d x - (x y + y) d y

e x p an d tan (4 x) (1 + sin (x) - 1 = 0)

e x p an d e^{- 3 x} (\frac{e ^{3 x} x}{3} - e^{3 x}) + \frac{1}{5} e^{5 x}