Implicit Differentiation concept help?

[shocklightnin]

Homework Statement

Its not homework, i have the answer I am just having a hard time wrapping my head around the concept of differentiating implicitly defined functions.

the question was: x^3+y^3=3xy, find the equation of the tangent line at the point (3/2,3/2).

Homework Equations

x^3+y^3=3xy

The Attempt at a Solution

so what my prof did was:
1)x^3+y^3=3xy
2)3x^2+3y^2(dy/dx)=3y+3x(dy/dx)

i get the part on the left, but i don't understand how he got the part on the right... :/

if anyone could just elaborate on the steps in between those two it would be much appreciated for my understanding. thank you.

 

[shocklightnin]

ah nevermind I got it, silly really. how can i delete this thread?

 

[Dick]

Your prof used the product rule on the right side.

 

[shocklightnin]

yeah. i feel extremely silly for asking. I've been staring at the screen for too long at these examples. any way to delete this cause its 'solved'? or do i just sort of leave it.

 

[Dick]

yeah. i feel extremely silly for asking. I've been staring at the screen for too long at these examples. any way to delete this cause its 'solved'? or do i just sort of leave it.

Oh, just leave it. It's no big deal. Everybody has their silly moments. Sometimes just posting a question helps you think.

 

[shocklightnin]

Yeah, typing it out defs helped. Alright, just going to leave it then.