展开 y'(x)(x+y-2)^2

解答

展开

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

x^{2} y' (x) + 2 x y' (x) y - 4 x y' (x) + y' (x) y^{2} - 4 y' (x) y + 4 y' (x)

求解步骤

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

(x + y - 2)^{2} = x^{2} + 2 x y - 4 x + y^{2} - 4 y + 4

= y^{^{'}} (x) (x^{2} + 2 x y - 4 x + y^{2} - 4 y + 4)

打开括号

= y^{^{'}} (x) x^{2} + y^{^{'}} (x) 2 x y + y^{^{'}} (x) (- 4 x) + y^{^{'}} (x) y^{2} + y^{^{'}} (x) (- 4 y) + y^{^{'}} (x) 4

使用加减运算法则

+ (- a) = - a

= x^{2} y^{^{'}} (x) + 2 x y^{^{'}} (x) y - 4 x y^{^{'}} (x) + y^{^{'}} (x) y^{2} - 4 y^{^{'}} (x) y + 4 y^{^{'}} (x)

e x p an d \frac{36 ( 7 x - y ) ( x + 7 y )}{25}

e x p an d \frac{3}{2 ( 2 t - 1 )}

e x p an d \frac{1}{5 x}

e x p an d (6 x - 2 y = 1, 2) (12 x - 4 y = 14)

e x p an d \frac{10}{s ( s ^{2} + 4 )}