`x^(2/3) + y^(2/3) = 5, (8,1)` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

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GivenĀ `x^(2/3)+y^(2/3)=5, (8,1)`

` (2/3)x^(-1/3)+(2/3)y^(-1/3)dy/dx=0 `

`(2/3)y^(-1/3)dy/dx=-(2/3)x^(-1/3)`

`dy/dx=-(x^(-1/3))/(y^(-1/3))`

`dy/dx=-(y^(1/3)/x^(1/3))`

`dy/dx=-(1)^(1/3)/(8)^(1/3)`

`dy/dx=-1/2`