`y^2 = x^3` Find the second derivative implicitly in terms of `x` and `y`.

Textbook Question

Chapter 2, 2.5 - Problem 49 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `y^2=x^3`

`2ydy/dx=3x^2`

`dy/dx=(3x^2)/(2y)`

`(d^2y)/dx^2=((2y)(6x)-(3x^2)(2)dy/dx)/(2y)^2`

`(d^2y)/dx^2=[(12xy)-(6x^2)(3x^2)/(2y)]/(4y^2)`

`(d^2y)/dx^2=((12xy^2-9x^4)/y)(1/(4y^2))`

`(d^2y)/dx^2=(12xy^2-9x^4)/(4y^3)`

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