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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

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

Simplify

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}

(S g n (x^{2} - 1)) x - 1 + 1

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

2 \cdot 2 \cdot 2 \cdot 2

(t^{3} + e^{4 t}) d t

- 4 x^{2} (x y^{2} + 3 x^{-} 4)

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