Question

find dy/dx where xy^3-3x^2=7y

Answer 1

(y^3 -6x) / (3y^2-7)

Answer 2

I am not sure how to work it. I just started working on these kind of problems.
My examples are confusing.
I have (x+3xy) -3x^2=7 to start off with, is that correct?

Answer 3

No, this is partial differentiation,

it is not like other differentiation

Answer 4

Its Implicit differentiation, partials are when you hold one variable as a constant. In Implicit differentiation you take the derivative of both variables with respect to x.

Answer 5

here's the work:
\[xy^3-3x^2=7y \rightarrow y^3+3xy^2\frac{dy}{dx}-6x=7\frac{dy}{dx}\]
\[\rightarrow y^3-6x=7\frac{dy}{dx}-3xy^2\frac{dy}{dx}\]
\[\rightarrow y^3-6x=(7-3xy^2)\frac{dy}{dx}\]
\[\frac{dy}{dx}=\frac{y^3-6x}{7-3xy^2}\]