$\dfrac{d}{dx}{\, \coth{x}} \,=\, -\operatorname{csch}^2{x}$
When a variable is denoted by $x$, the hyperbolic cotangent function is written as $\coth{(x)}$ in mathematics. The derivative of the hyperbolic function with respect to $x$ is written in the following mathematical form in differential calculus.
$\dfrac{d}{dx}{\, \coth{x}}$
The derivative of the hyperbolic cotangent function is equal to the negative square of hyperbolic co-secant function.
$\implies$ $\dfrac{d}{dx}{\, \coth{(x)}} \,=\, -\operatorname{csch}^2{(x)}$
The derivative rule of hyperbolic cotangent function can also be written in terms of any variable.
$(1) \,\,\,$ $\dfrac{d}{dl}{\, \coth{(l)}} \,=\, -\operatorname{csch}^2{(l)}$
$(2) \,\,\,$ $\dfrac{d}{dp}{\, \coth{(p)}} \,=\, -\operatorname{csch}^2{(p)}$
$(3) \,\,\,$ $\dfrac{d}{dz}{\, \coth{(z)}} \,=\, -\operatorname{csch}^2{(z)}$
Learn how to prove the derivative formula of the hyperbolic cotangent function from the first principle of the differentiation.
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