`x^2 - y^2 = 36` Find the second derivative implicitly in terms of `x` and `y`.

Textbook Question

Chapter 2, 2.5 - Problem 47 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`x^2 - y^2 = 36`

`or, 2x - 2y(dy/dx) = 0`

`or, dy/dx = x/y`

``Now,

differentiating again we get

`2 - 2y((d^2y)/dx^2) - 2(dy/dx)^2 = 0`

`or, 2 - 2y((d^2y_/dx^2) - 2(x^2/y^2) = 0`

`or, (d^2y)/dx^2 = (y^2 - x^2)/y^3`

``

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