$\dfrac{d}{dx}{\, \coth{x}} \,=\, -\operatorname{csch}^2{x}$

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.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.