Question

If y=x+√(x²-1), then y-x(dy/dx) = ???

Answer 1

If y=x+√(x²-1), then y-x(dy/dx) = ???

$\textbf{Given:}$

$y=x+\sqrt{x^2-1}$

$\textbf{To find:}$

$y-x\dfrac{dy}{dx}$

$\textbf{Solution:}$

$\text{Consider,}$

$y=x+\sqrt{x^2-1}$

$\text{Differentiate with respect to 'x'}$

$\dfrac{dy}{dx}=1+\dfrac{2x}{2\sqrt{x^2-1}}$

$\dfrac{dy}{dx}=1+\dfrac{x}{\sqrt{x^2-1}}$

$\text{Now,}$

$y-x\dfrac{dy}{dx}$

$=(x+\sqrt{x^2-1})-x(1+\dfrac{x}{\sqrt{x^2-1}})$

$=\sqrt{x^2-1}-\dfrac{x^2}{\sqrt{x^2-1}}$

$=\dfrac{(x^2-1)-x^2}{\sqrt{x^2-1}}$

$=\dfrac{-1}{\sqrt{x^2-1}}$

$\implies\boxed{\bf\,y-x\dfrac{dy}{dx}=\dfrac{-1}{\sqrt{x^2-1}}}$

Find more:

1.Y = (tan x +cot x)/ (tan x - cotx ) then dy/dx =?

https://brainly.in/question/3429497

2.If y=√x+1/√x show that 2x d y /dx +y =2√x

https://brainly.in/question/5156094

3.If y = tan^–1(sec x + tan x), then find dy/dx.

https://brainly.in/question/8085217

4.If y= log tan(π/4+x/2),show that dy/dx=secx

https://brainly.in/question/5012403

5.Y=xtanx,show that xsin^2x(dy/dx)=x^2 tan x +y sin^2 x

https://brainly.in/question/16864243