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If Ey ( X +1) = 1, Then Show that D 2 Y D X 2 = ( D Y D X ) 2 . - Mathematics

Sum

If ey ( x +1)  = 1, then show that  `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`

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Solution

We have, 

ey ( x +1)  = 1

⇒ ey = `1/(x + 1)` 

⇒ log `e^y = log (1/(x+1))`

⇒ y = - log (x + 1) 

` ⇒ (dy)/(dx) = - 1/ (x + 1) and (d^2 y) /(dx^2) = 1/((x + 1)^2)`

` ⇒  (d^2 y)/(dx^2) = ((dy)/(dx))^2`

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