# 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.

So:

Next, we can differentiate the right side using the chain rule. In short terms, the chain rule is:

- The derivative of the outer function, with the inner function plugged in...
- ...multiplied by the derivative of the inner function.

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To differentiate xy = cot(xy), we'll use implicit differentiation.

The derivative of xy with respect to x is y + x(dy/dx).

The derivative of cot(xy) with respect to x is -csc^2(xy) * (y + x(dy/dx)).

Now, equating the derivatives, we get:

y + x(dy/dx) = -csc^2(xy) * (y + x(dy/dx)).

Solving for dy/dx, we get:

dy/dx = - (y + x(dy/dx)) / (x + y*csc^2(xy)).

This is the derivative of xy = cot(xy) with respect to x.

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