What is expand (d^2x)/(d^2y)(4y^3=6x^2+1) ?

The solution to expand (d^2x)/(d^2y)(4y^3=6x^2+1) is 4xy^2=6x^2+x/y

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expand (d^2x)/(d^2y)(4y^3=6x^2+1)

expand

\frac{d ^{2} x}{d ^{2} y} (4 y^{3} = 6 x^{2} + 1)

4 x y^{2} = 6 x^{2} + \frac{x}{y}

Solution steps

\frac{d ^{2} x}{d ^{2} y} (4 y^{3} = 6 x^{2} + 1)

= \frac{d ^{2} x}{d ^{2} y} (4 \cdot 6 = x^{2} y^{3} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{d ^{2} x}{d ^{2} y}, b = 4 y^{3} = 6 x^{2}, c = 1

\frac{d ^{2} x}{d ^{2} y} \cdot 4 y^{3} = 6 x^{2} + \frac{d ^{2} x}{d ^{2} y} \cdot 1

4 \cdot \frac{d ^{2} x}{d ^{2} y} y^{3} = 6 x^{2} + 1 \cdot \frac{d ^{2} x}{d ^{2} y}

Simplify

4 \cdot \frac{d ^{2} x}{d ^{2} y} y^{3} = 6 x^{2} + 1 \cdot \frac{d ^{2} x}{d ^{2} y} : 4 x y^{2} = 6 x^{2} + \frac{x}{y}

4 x y^{2} = 6 x^{2} + \frac{x}{y}

(4 + x) (4 - x)

(x - 10) x + 100

\frac{2 ( 2 n - 2 x )}{n ^{2}}

- 1 (3 x + 3 y = 24)

\frac{2}{x ( x + 5 a ) ( x + 6 a )}

What is expand (d^2x)/(d^2y)(4y^3=6x^2+1) ?
The solution to expand (d^2x)/(d^2y)(4y^3=6x^2+1) is 4xy^2=6x^2+x/y