Question

Using implicit differentiation find dy/dx of tan (x+y)=(x-y).

Answer 1

Use the chain rule. Remember that [g(y)]'=y' g'(y)

Answer 2

I don't have any real good examples of using the chain rule with implicit differentiation. Kind of one of those that the prof thought he could teach us in the last 5 mins of class before spring break.

Answer 3

For example g(xy)=g'(xy)(xy)'=g'(xy)(y+xy')

Answer 4

I'm so confused with this.

Answer 5

What part?

Answer 6

All of it!

Answer 7

Say you have xy=sin(xy). You differentiate both sides with respect to x
(xy)'=(sin(xy))'
Now we know that d/dx(y)=dy/dx=y'
Using the product rule on the left we have
y+xy'=(sin(xy))'
On the left we have a composition. sin(x) and xy
So we have
y+xy'=cos(xy)*(xy)'
Like we did on the left, use product rule for (xy)'
y+xy'=(y+xy')cos(xy)
Then solve for y'

Answer 8

That is much simpler than what I have in my notes :)