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प्रश्न
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) =((dy)/(dx))^2`
उत्तर
Given, ey (x + 1) = 1 ...(1)
or, (x + 1) ey = 1
Differentiating both sides with respect to x,
⇒ `1 · ey + (x + 1) ey dy/dx = 0`
`=> e^y + 1 * dy/dx = 0` .... [Putting the value of ey(x + 1) from equation (1)]
`=> dy/dx = - e^y`
Differentiating both sides again with respect to x,
`(d^2 y)/dx^2 = -e^y dy/dx` ...(putting -ey = `dy/dx`)
`= (dy/dx)(dy/dx) = (dy/dx)^2`
Hence, `(d^2 y)/dx^2 = (dy/dx)^2`
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