If y=x+√(x²-1), then y-x(dy/dx) = ???

1.	If y=x+√(x²-1), then y-x(dy/dx) = ???
Answer» If y=X+√(x²-1), then y-x(dy/dx) = ??? $\textbf{Given:}$ $y=x+\sqrt{x^2-1}$ $\textbf{To <klux>FIND</klux>:}$ $y-x\dfrac{dy}{dx}$ $\textbf{Solution:}$ $\text{Consider,}$ $y=x+\sqrt{x^2-1}$ $\text{Differentiate with respect to 'x'}$ $\dfrac{dy}{dx}=1+\dfrac{<klux>2X</klux>}{2\sqrt{x^2-1}}$ $\dfrac{dy}{dx}=1+\dfrac{x}{\sqrt{x^2-1}}$ $\text{Now,}$ $y-x\dfrac{dy}{dx}$ $=(x+\sqrt{x^2-1})-x(1+\dfrac{x}{\sqrt{x^2-1}})$ $=\sqrt{x^2-1}-\dfrac{x^2}{\sqrt{x^2-1}}$ $=\dfrac{(x^2-1)-x^2}{\sqrt{x^2-1}}$ $=\dfrac{-1}{\sqrt{x^2-1}}$ $\implies\boxed{\bf\,y-x\dfrac{dy}{dx}=\dfrac{-1}{\sqrt{x^2-1}}}$ Find more: 1.Y = (tan x +COT x)/ (tan x - COTX ) then dy/dx =? brainly.in/question/3429497 2.If y=√x+1/√x show that 2x d y /dx +y =2√x brainly.in/question/5156094 3.If y = tan^–1(sec x + tan x), then find dy/dx. brainly.in/question/8085217 4.If y= log tan(π/4+x/2),show that dy/dx=secx brainly.in/question/5012403 5.Y=xtanx,show that xsin^2x(dy/dx)=x^2 tan x +y sin^2 x brainly.in/question/16864243

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If y=X+√(x²-1), then y-x(dy/dx) = ???

$\textbf{Given:}$