`y^3 = 4x` Find the second derivative implicitly in terms of `x` and `y`.

Textbook Question

Chapter 2, 2.5 - Problem 50 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `y^3=4x`

`3y^2dy/dx=4`

`dy/dx=(4)/(3y^2)=(4y^-2)/3`

` `

`(d^2y)/dx^2=(-2)(4/3)(y^-3)dy/dx`

` (d^2y)/dx^2=-8/(3y^3)dy/dx`

`(d^2y)/dx^2=[(-8)/(3y^3)][4/(3y^2)]`

`(d^2y)/dx=-32/(9y^5)`

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