How do you know when to apply product rule and when to apply chain rule?

For the problem xy+2x+3y^3=x^5+2

my instructor applied product rule to xy and chain rule to 3y^3. How can I tell the difference?

Question

How do you know when to apply product rule and when to apply chain rule?

For the problem xy+2x+3y^3=x^5+2

my instructor applied product rule to xy and chain rule to 3y^3. How can I tell the difference?

anonymous · Answer

Are you taking a derivative or what?

anonymous · Answer

Yes, a derivative.

anonymous · Answer

Oh! You go to Tech! I go to Kennesaw, haha.

anonymous · Answer

Oh nice. I'm guessing I don't know you. You apply product rule to xy because you have two variables x and y. You apply chain rule to y^3 because y is a function of x, so the derivative of y^3 is 3y^2*dy/dx

anonymous · Answer

Ohhhhh I see now. Thanks a lot for your help!

anonymous · Answer

No problem. It'd be great if you could fan me. ;D

anonymous · Answer

Definitely! Especially since you're just down the road :) I have a lot of friends that go to Tech. Maybe I'll see you around. They're architecture majors though.

anonymous · Answer

Oh haha... Maybe I will see you around. I know a few architecture majors myself. My fb id is hanky.mei. Let me know if we have mutual friends.