How do you differentiate #xy = cot(xy)#?
Start off by differentiating both sides.
First, let's discuss how to differentiate the left side.
We can apply the product rule.
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.
We've already solved
Then we need to isolate
Then we factor out