$\dfrac{d}{dx}{\, \operatorname{sech}{x}}$ $\,=\,$ $-\operatorname{sech}{x}\tanh{x}$
When $x$ represents a variable, the hyperbolic secant function is written as $\operatorname{sech}{x}$ in mathematical form. The derivative of the hyperbolic secant function with respect to $x$ is written in below form in differential calculus.
$\dfrac{d}{dx}{\, \operatorname{sech}{x}}$
The differentiation formula of the hyperbolic secant function is simply written mathematically as $(\operatorname{sech}{x})’$ in calculus. The differentiation of the hyperbolic secant function is equal to the negative sign of product of hyperbolic secant and tangent functions.
$\implies$ $\dfrac{d}{dx}{\, \operatorname{sech}{x}}$ $\,=\,$ $-\operatorname{sech}{x}\tanh{x}$
Mathematically, the derivative of hyperbolic secant function can also be written in terms of any variable in differential calculus.
$(1) \,\,\,$ $\dfrac{d}{dl}{\, \operatorname{sech}{(l)}}$ $\,=\,$ $-\operatorname{sech}{(l)}\tanh{(l)}$
$(2) \,\,\,$ $\dfrac{d}{dq}{\, \operatorname{sech}{(q)}}$ $\,=\,$ $-\operatorname{sech}{(q)}\tanh{(q)}$
$(3) \,\,\,$ $\dfrac{d}{dy}{\, \operatorname{sech}{(y)}}$ $\,=\,$ $-\operatorname{sech}{(y)}\tanh{(y)}$
Learn how to prove the differentiation of hyperbolic secant in differential calculus from the first principle of differentiation.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the maths problems in different methods with understandable steps.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved