) Given: ln y = 2y2 – x.  Find y ‘and evaluate y ‘ at (2, 1).

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Math

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Use the chain rule for implicit differentiation:


`"ln" y = 2y^2 - x `

`(1)/(y) y' = 4 y y' -1`

`((1)/(y) - 4y) y' = -1`

`y' = (-1)/((1)/(y) - 4y)=(-y)/(1-4y^2)=(y)/(4y^2-1)`

At (2,1),

`y' = (1)/(4(2)^2-1)=(1)/(15)`

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