What is expand (3x^2y+2xy+y^3)+(x^2+y^2)y'(x) ?

The solution to expand (3x^2y+2xy+y^3)+(x^2+y^2)y'(x) is 3x^2y+2xy+y^3+x^2y'(x)+y'(x)y^2

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expand (3x^2y+2xy+y^3)+(x^2+y^2)y'(x)

expand

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

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

Solution steps

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

Expand

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

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

Remove parentheses:

(a) = a

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

\frac{d ^{2}}{d t ^{2}} ((x) (cos (2 t) + sin (2 t) + \frac{1}{5} e^{t}))

- 3 (x - \frac{π}{3})

\frac{\partial}{\partial x} ((z) (x y - 2 x + 5 y))

(2 x - y) (3 x + 5 y)

lo g_{10} (1)

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