Question

How do you differentiate `5xy + y^3 = 2x + 3y`?

Answer 1

I found: `(dy)/(dx)=(2-5y)/(5x+3y^2-3)`

Explanation:

You can use implicit differentiation rememberig that `y` represents a function of `x` and needs to be differentiated accordingly;
for example: if you have `y^2` you differentiate it to get:
`2y*(dy)/(dx)` where you use `(dy)/(dx)` to take into account the dependence with `x`.
In your case you get:
`5y+5x(dy)/(dx)+3y^2(dy)/(dx)=2+3(dy)/(dx)`
collect `(dy)/(dx)`:
`(dy)/(dx)(5x+3y^2-3)=2-5y`
and:
`(dy)/(dx)=(2-5y)/(5x+3y^2-3)`