Question

obtenga la derivada de las siguiente funcione, utilizando las formulas de derivación

Answer 1

Para resolver la siguiente derivada recordemos algunas fórmulas generales de derivación:

              $\begin{array}{c}\boxed{\boldsymbol{\sf{\dfrac{d}{dx}\left(\dfrac{u}{v}\right)=\dfrac{v\dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^2}}}}\end{array}\quad \Longrightarrow\quad\sf{F\acute{o}rmula\ 1}$

              $\begin{array}{c}\boxed{\boldsymbol{\sf{\dfrac{d}{dx}(u+v)=\dfrac{d}{dx}(u)+\dfrac{d}{dx}(v)}}}\end{array}\quad \Longrightarrow\quad\sf{F\acute{o}rmula\ 2}$

              $\begin{array}{c}\boxed{\boldsymbol{\sf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}\end{array}\quad \Longrightarrow\quad\sf{F\acute{o}rmula\ 3}$

              $\begin{array}{c}\boxed{\boldsymbol{\sf{\dfrac{d}{dx}(C)=0}}}\end{array},\sf{C=cte}\quad \Longrightarrow\quad\sf{F\acute{o}rmula\ 4}$

Entonces en el problema

   $\begin{array}{ccl}\sf{f(x)=\dfrac{2}{x^2 - 1}}&&\sf{\gray{\%\ Aplicamos\ la\ f\acute{o}rmula\ 1}}\\\\\sf{\dfrac{d}{dx}f(x)=\dfrac{(x^2-1)\dfrac{d(2)}{dx}-(2)\dfrac{d(x^2-1)}{dx}}{(x^2-1)^2}}&&\sf{\gray{\%\ Aplicamos\ la\ f\acute{o}rmula\ 4\ y\ 2}}\\\\\sf{\dfrac{d}{dx}f(x)=\dfrac{(x^2-1)(0)-2\left(\dfrac{dx^2}{dx}-\dfrac{d(1)}{dx}\right)}{(x^2-1)^2}}&&\sf{\gray{\%\ Aplicamos\ la\ f\acute{o}rmula\ 4\ y\ 3}}\\\\\vphantom{A}\sf{\dfrac{d}{dx}f(x)=\dfrac{0-2(2x^{2-1}-0)}{(x^2-1)^2}}&&\\\\\boxed{\boxed{\boldsymbol{\sf{\dfrac{d}{dx}f(x)=-\dfrac{4x}{(x^2-1)^2}}}}}&&\end{array}[\tex]</p><p></p><p></p><p>                                             [tex]\boxed{\sf{{R}}\quad\raisebox{10pt}{ \sf{\red{O}} }\!\!\!\!\raisebox{-10pt}{ \sf{\red{O}} }\quad\raisebox{15pt}{ \sf{{G}} }\!\!\!\!\raisebox{-15pt}{ \sf{{G}} }\quad\raisebox{15pt}{ \sf{\red{H}} }\!\!\!\!\raisebox{-15pt}{ \sf{\red{H}} }\quad\raisebox{10pt}{ \sf{{E}} }\!\!\!\!\raisebox{-10pt}{ \sf{{E}} }\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}$