What is expand (12y+12xy'(x))y'(x) ?

The solution to expand (12y+12xy'(x))y'(x) is 12y'(x)y+12x(y'(x))^2

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expand (12y+12xy'(x))y'(x)

expand

(12 y + 12 x y^{'} (x)) y^{'} (x)

12 y' (x) y + 12 x (y' (x))^{2}

Solution steps

(12 y + 12 x y^{'} (x)) y^{'} (x)

Apply the distributive law:

a (b + c) = ab + a c

a = y^{'} (x), b = 12 y, c = 12 x y^{'} (x)

= y^{^{'}} (x) 12 y + y^{^{'}} (x) 12 x y^{^{'}} (x)

= 12 y^{^{'}} (x) y + 12 x y^{^{'}} (x) y^{^{'}} (x)

12 x y^{'} (x) y^{'} (x) = 12 x (y^{'} (x))^{2}

= 12 y^{^{'}} (x) y + 12 x (y^{^{'}} (x))^{2}

\frac{( x + 1 ) ^{2}}{63}

- 9 (x - 3) (x - 1)

tan (y) sin (y) + cos (y)

\frac{( e ^{- s} + s )}{s \cdot ( s - 3 ) ( s - 2 )}

14 (- 2 - 2 t)^{2} \cdot 3 t

What is expand (12y+12xy'(x))y'(x) ?
The solution to expand (12y+12xy'(x))y'(x) is 12y'(x)y+12x(y'(x))^2