`y^3 - x^2 = 4, (2,2)` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

Textbook Question

Chapter 2, 2.5 - Problem 22 - 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-x^2=4`

`3y^2dy/dx-2x=0`

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

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

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

`dy/dx=4/12=1/3`

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