# How do you differentiate #xy = cot(xy)#?

##### 1 Answer

#### Explanation:

Start off by differentiating both sides.

First, let's discuss how to differentiate the left side.

We can apply the product rule.

So:

Next, we can differentiate the right side using the chain rule.

In short terms, the chain rule is:

1) The derivative of the outer function, with the inner function plugged in...

2) ...multiplied by the derivative of the inner function.

The outer function is

The inner function is

The derivative of the outer function is

Plug in the inner function and we get

Then we multiply this by the derivative of the inner function.

So

We've already solved

Then we need to isolate

Then we factor out