C3 Implicit Differentiation Help

Hi.
I am doing a C3 paper (link: http://www.mei.org.uk/files/papers/c308ju_fg48.pdf)

Anyway, i am stuck on Q7. I am ok with the method of implicit differentiation. Differentiate x terms and y terms, and stick a dy/dx after the y terms. Then you rearrange etc. However, i am slightly confused when on the part where i need to differentiate xy. I would use the product rule, however, when using the product rule, im unsure where the dy/dx goes

so i have x^2 + xy+y^2=12
i would do 2x+x+y(dy/dx)+2y(dy/dx)=0
but this is wrong
Help??
thanks

Look at this bit again

Ok. i have differentiated 'xy' using the product rule, which gives me x+y.
Surely i stick the dy/dx after the y???

$\dfrac{\mathrm{d}}{\mathrm{d}x}xy=x \times \dfrac{\mathrm{d}}{\mathrm{d}x}y + y \times \dfrac{\mathrm{d}}{\mathrm{d}x}x$

Do you see why that's the case?

Can you do the next step?

Ok. i have differentiated 'xy' using the product rule, which gives me x+y.
Surely i stick the dy/dx after the y???

Ok. i have differentiated 'xy' using the product rule, which gives me x+y.
Surely i stick the dy/dx after the y???

So with implicit differentiation, when you used the product rule, dy/dx of y alone will simply be dy/dx (1)

Might want to be careful there, it's $\frac{\mathrm{d}}{\mathrm{d}x}$ of $y$ - the derivative is an operator.