x^2+3xy+y^2

x^2y^3 - 6xy^2 = 10

Yes, we do offer free help, but not 'free answers'... =/

Do you know how to differentiate an expression with one variable?

\frac{d}{dx}(2x^2 + 1) = 4x

So, you can express the derivative of what you got as:

\frac{d}{dx}(x^2+3xy+y^2) = \frac{d}{dx}(x^2)
\frac{d}{dx}(3xy) + \frac{d}{dx}(y^2)

You can differentiate the first part?

For the second part, let me give you an example.

\frac{d}{dx}(4y + y^2) = 4 \frac{dy}{dx} + 2y\frac{dy}{dx}

As you can see, you differentiate the y similar to how you differentiate x, but you just add dy/dx after differentiating.

For the middle part of your problem, use the product rule.

If I may. Allow me to show a method I often use for implicit diff.

Use \frac{-F_{x}}{F_{y}}

i.e. x^{2}y^{3}-6xy^{2}=10

-F_{x}=-2y^{2}(xy-3)

F_{y}=3xy(xy-4)

\frac{-F_{x}}{F_{y}}=y'=\frac{-2y(xy-3)}{3x(xy-4)}

Just a thought if anyone is interested.

I wasn't sure what you did at first, but when I expanded it, I understood. Interesting method :)

You only missed a 'y' in the denominator ;)