Implicit differentiation question: x^2 + y^3 = 3

[MarkSA]

If I have a problem that is stated in the following format:

"Find the derivative of:"
1) x^2 + y^3 = 3

Since it is not asking for the derivative with respect to x or y, would the proper answer then be:

2x(x') + (3y^2)y' = 0?

Or would it be:

2x + (3y^2)y' = 0?

Thanks.

 

[soroban]

Hello, Mark!

I have a problem that is stated in the following format:

"Find the derivative of: .x^2 + y^3 = 3"

Since it is not asking for the derivative with respect to x or y,

would the proper answer then be: .2x(x') + (3y^2)y' = 0? . . . . with respect to what?

Or would it be: .2x + (3y^2)y' = 0? . . . . yes!

\(\displaystyle \text{Conventionally, "the derivative" refers to }\:\frac{dy}{dx}\)
. . \(\displaystyle \text{but the problem should have specified.}\)