Question

Si f'(x)=×/×-1 , y=f(×-1/×+1) , hallar dy/dx

Answer 1

                          $y=f\circ g(x) \,,\, g(x)=\dfrac{x-1}{x+1}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{dy}{dg}\cdot\dfrac{dg}{dx}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{g}{g-1}\cdot \dfrac{2}{(x+1)^2}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{\dfrac{x-1}{x+1}}{\dfrac{x-1}{x+1}-1}\cdot \dfrac{2}{(x+1)^2}\\ \\ \\ \dfrac{dy}{dx}=\dfrac{x-1}{-2}\cdot \dfrac{2}{(x+1)^2}\\ \\ \\ \boxed{\dfrac{dy}{dx}=\dfrac{1-x}{(x+1)^2}}$