Question

How do you find `(dy)/(dx)` given `-2y^2+3=x^3`?

Answer 1

`\frac{dy}{dx}=-\frac{3x^2}{4y}`

Explanation:

Differentiate both sides as such:
`\frac{d}{dx}(-2y^{2}+3)=\frac{d}{dx}(x^{3})`
this leads to:

`-2\frac{d}{dx}(y^{2})=3x^{2}`

`-2(2y\frac{dy}{dx})=3x^{2}`

rearrange to make `\frac{dy}{dx}` the factor to get:

`\frac{dy}{dx}=-\frac{3x^{2}}{4y}`