展开 (x+y)(3y^2y'(x))

解答

展开

(x + y) (3 y^{2} y^{'} (x))

3 x y^{2} y' (x) + 3 y' (x) y^{3}

求解步骤

(x + y) (3 y^{2} y^{'} (x))

使用分配律:

a (b + c) = ab + a c

a = (3 y^{2} y^{'} (x)), b = x, c = y

= (3 y^{2} y^{^{'}} (x)) x + (3 y^{2} y^{^{'}} (x)) y

= x (3 y^{2} y^{^{'}} (x)) + (3 y^{2} y^{^{'}} (x)) y

化简

x (3 y^{2} y^{'} (x)) + (3 y^{2} y^{'} (x)) y : 3 x y^{2} y^{'} (x) + 3 y^{'} (x) y^{3}

= 3 x y^{2} y^{'} (x) + 3 y^{'} (x) y^{3}

e x p an d (S g n (x^{2} - 1)) x - 1 + 1

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

e x p an d 2 \cdot 2 \cdot 2 \cdot 2

e x p an d (t^{3} + e^{4 t}) d t

e x p an d - 4 x^{2} (x y^{2} + 3 x^{-} 4)