Using 4x^2 - 9y^2 = 36

Question

Find y by implicit differentiation and then solve the equation explicitly for y and differentiate to get y' in terms of x.

Answer 1

I am sure you wanted y'

8x - 18y dy/dx = 0
-18y dy/dx = -8x
dy/dx = 8x/(18y) = 4x/(9y)

-9y^2 = 36 - 4x^2
y^2 = (4x^2 - 36)/9
y = (4x^2 - 36)^(1/2) /3
dy/dx = (1/6) (4x^2 - 36)^(-1/2) (8x)
= (4/3)(x)(4x^2 - 36)^(-1/2)