Question

If e^y (x+1) =1 , show that d^2y/dx^2 = (dy/dx)^2

Answer 1

$\textbf{Hello Mate.....}$

$\textbf{Question}$>>>>If e^y (x+1) =1 ,
show that d^2y/dx^2 = (dy/dx)^2

$\e^y$ (x+1) =1..........(i)

$\textbf{Answer}$>>>>

Differentiate Both Sides w.r.t x in eq. (i)

we apply here Multiplicate rule of derivative, so we get>>>>

$\{e}^y$ . $\frac{dy}{dx}$ ( x + 1 ) + $\frac{d( x+ 1)}{dx}$ . $\{e}^y$ = 0

$\{e}^y$ . $\frac{dy}{dx}$ ( x + 1 ) + $\{e}^y$ = 0

$\{e}^y$ . $\frac{dy}{dx}$ ( x + 1 ) = - $\{e}^y$

we cut $\{e}^y$ with $\{e}^y$ so we get>>>>

$\frac{dy}{dx}$ = $\frac{-1}{x + 1 }$

for further please check the attachment...

Hence Proved....

Be BrAinly...

@karangrover12