Consider the following equation. 6x^2 − y^2 = 4

Question

Find y'

 by implicit differentiation.

Solve the equation explicitly for y and differentiate to get y'

 in terms of x.

Answer 1

6x²-y²=4

12x-2yy'=0

y'=12x/2y = 6x/y

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y = √(6x²-4)

y' = 12x/(2√(6x²-4))=12x/(2y) = 6x/y = 6x/√(6x²-4)