What is expand (-4x^3+3y)(dx)/(dy) ?

The solution to expand (-4x^3+3y)(dx)/(dy) is -4x^3(dx)/(dy)+3y(dx)/(dy)

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expand (-4x^3+3y)(dx)/(dy)

expand

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

- 4 x^{3} \frac{d x}{d y} + 3 y \frac{d x}{d y}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{d x}{d y}, b = - 4 x^{3}, c = 3 y

= \frac{d x}{d y} (- 4 x^{3}) + \frac{d x}{d y} 3 y

Apply minus-plus rules

+ (- a) = - a

= - 4 x^{3} \frac{d x}{d y} + 3 y \frac{d x}{d y}

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

(x + i y)^{6} + (x + i y)^{3} - 1

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

(x - 2 - 5) (x - 2 + 5)

(1 - 2 y i)^{2}

What is expand (-4x^3+3y)(dx)/(dy) ?
The solution to expand (-4x^3+3y)(dx)/(dy) is -4x^3(dx)/(dy)+3y(dx)/(dy)