information:extraction
Using implicit differentiation

Let

Then

(The absolute value in the expression is necessary as the product of cosecant and cotangent in the interval of y is always nonnegative, while the radical x 2 − 1 {\displaystyle {\sqrt {x^{2}-1}}} is always nonnegative by definition of the principal square root, so the remaining factor must also be nonnegative, which is achieved by using the absolute value of x.)