What is expand 2x^2*((1+x^2)y'(x)+4xy) ?

The solution to expand 2x^2*((1+x^2)y'(x)+4xy) is 2x^2y'(x)+2x^4y'(x)+8x^3y

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expand 2x^2*((1+x^2)y'(x)+4xy)

expand

2 x^{2} \cdot ((1 + x^{2}) y^{'} (x) + 4 x y)

2 x^{2} y' (x) + 2 x^{4} y' (x) + 8 x^{3} y

Solution steps

2 x^{2} ((1 + x^{2}) y^{'} (x) + 4 x y)

Apply the distributive law:

a (b + c) = ab + a c

a = 2 x^{2}, b = (1 + x^{2}) y^{'} (x), c = 4 x y

= 2 x^{2} (1 + x^{2}) y^{^{'}} (x) + 2 x^{2} \cdot 4 x y

= 2 x^{2} (1 + x^{2}) y^{^{'}} (x) + 2 \cdot 4 x^{2} x y

Simplify

2 x^{2} (1 + x^{2}) y^{'} (x) + 2 \cdot 4 x^{2} x y : 2 x^{2} y^{'} (x) + 2 x^{4} y^{'} (x) + 8 x^{3} y

= 2 x^{2} y^{'} (x) + 2 x^{4} y^{'} (x) + 8 x^{3} y

\frac{( x + 8 ) ^{2}}{2}

\frac{9 - x}{x ( 2 x - 5 ) ( x - 4 )}

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

(1 - x) ln^{x} (x)

\frac{ln ( n + 1 )}{( n + 1 ) ^{2}}

What is expand 2x^2*((1+x^2)y'(x)+4xy) ?
The solution to expand 2x^2*((1+x^2)y'(x)+4xy) is 2x^2y'(x)+2x^4y'(x)+8x^3y