This is an implicit function.

3 cot(x + y) = cos y²

For the left hand side, we put u = x + y.

Differentiating 3 cot u gives us:

Substituting for u and performing the du/dx gives us:

On the right hand side, we let u = y². Differentiating cos u gives us:

Substituting for u and performing the du/dx part gives us:

We put both sides together:

Expanding gives:

Adding

to both sides:

Adding

to both sides:

Factoring out the dy/dx term:

This gives us: