First off i have a problem that the teacher somewhat worked out on the board.

I am not sure how he got the answer.

Find the vector function that represents the curve of intersection of the two surfaces.

The cylinder.

$\displaystyle x^2 + y^2 = 4$

and the surface $\displaystyle z=xy$

Attempt:

$\displaystyle r=2$

$\displaystyle x= 2cost$

$\displaystyle y=2sint$

$\displaystyle z=(2cost)(2sint)$

Now, from here i think the teacher used the product rule? I am not sure.

Solving for z

$\displaystyle z=2sin2t$

I tried the product rule but couldnt get it. Could someone work out the steps on how he got the answer?

Thank you