Sum

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

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#### Solution

We have,

e^{y} ( x +1) = 1

⇒ e^{y} = `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`

Concept: Logarithmic Differentiation

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