展开 4x^{4x^2}(2xln(x)+x)

解答

展开

4 x^{4 x^{2}} (2 x ln (x) + x)

8 x^{1 + 4 x^{2}} ln (x) + 4 x^{1 + 4 x^{2}}

求解步骤

4 x^{4 x^{2}} (2 x ln (x) + x)

使用分配律:

a (b + c) = ab + a c

a = 4 x^{4 x^{2}}, b = 2 x ln (x), c = x

= 4 x^{4 x^{2}} \cdot 2 x ln (x) + 4 x^{4 x^{2}} x

= 4 \cdot 2 x x^{4 x^{2}} ln (x) + 4 x x^{4 x^{2}}

化简

4 \cdot 2 x x^{4 x^{2}} ln (x) + 4 x x^{4 x^{2}} : 8 x^{1 + 4 x^{2}} ln (x) + 4 x^{1 + 4 x^{2}}

= 8 x^{1 + 4 x^{2}} ln (x) + 4 x^{1 + 4 x^{2}}

e x p an d a b + (x - h)^{2} + k

\frac{\partial}{\partial x} ((f (x, y)) (y^{5} - 3 x y))

e x p an d \frac{( 8 x ^{6} - 9 ) ^{2}}{576 x ^{6}}

e x p an d 2 (e + \frac{1}{e} - 2)

e x p an d \frac{y + 2 z - x}{( y + 2 z ) ^{2}}