What is expand y'(x)(x+y-2)^2 ?

The solution to expand y'(x)(x+y-2)^2 is x^2y'(x)+2xy'(x)y-4xy'(x)+y'(x)y^2-4y'(x)y+4y'(x)

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expand y'(x)(x+y-2)^2

expand

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)

Solution steps

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)

Distribute parentheses

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

Apply minus-plus rules

+ (- 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)

\frac{36 ( 7 x - y ) ( x + 7 y )}{25}

\frac{3}{2 ( 2 t - 1 )}

\frac{1}{5 x}

(6 x - 2 y = 1, 2) (12 x - 4 y = 14)

\frac{10}{s ( s ^{2} + 4 )}

What is expand y'(x)(x+y-2)^2 ?
The solution to expand y'(x)(x+y-2)^2 is x^2y'(x)+2xy'(x)y-4xy'(x)+y'(x)y^2-4y'(x)y+4y'(x)