What is expand y^2(y+3x(dy)/(dx)) ?

The solution to expand y^2(y+3x(dy)/(dx)) is y^3+3y^2x(dy)/(dx)

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expand y^2(y+3x(dy)/(dx))

expand

y^{2} (y + 3 x \frac{d y}{d x})

y^{3} + 3 y^{2} x \frac{d y}{d x}

Solution steps

y^{2} (y + 3 x \frac{d y}{d x})

Apply the distributive law:

a (b + c) = ab + a c

a = y^{2}, b = y, c = 3 x \frac{d y}{d x}

= y^{2} y + y^{2} \cdot 3 x \frac{d y}{d x}

= y^{2} y + 3 y^{2} x \frac{d y}{d x}

y^{2} y = y^{3}

= y^{3} + 3 y^{2} x \frac{d y}{d x}

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

- \frac{7 x ^{2}}{( x - 6 ) ( x + 7 )}

f (3, - 1)

m u lt i pl y (x + 2) (x^{2} + 5)

(- 2 w^{4} X)^{3}

What is expand y^2(y+3x(dy)/(dx)) ?
The solution to expand y^2(y+3x(dy)/(dx)) is y^3+3y^2x(dy)/(dx)