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Question
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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