`x^2 + y^2 = 4` Find the second derivative implicitly in terms of `x` and `y`.

Textbook Question

Chapter 2, 2.5 - Problem 45 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`x^2+y^2=4`

differentiating both sides with respect to x,

`2x+2yy'=0`

`2yy'=-2x`

`y'=-x/y`

differentiating again both sides with respect to x and applying quotient rule,

`y''=-(y-xy')/y^2`

plugging in the value of y' in y'',

`y''=-(y-x(-x/y))/y^2`

`y''=-(y+x^2/y)/y^2`

`y''=-(y^2+x^2)/y^3`

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